# Last Year

Althaus, E., Beber, B., Damm, W., Disch, S., Hagemann, W., Rakow, A., … Wirtz, B. (2017). Verification of Linear Hybrid Systems with Large Discrete State Spaces Using Counterexample-guided Abstraction Refinement. Science of Computer Programming, 148. doi:10.1016/j.scico.2017.04.010
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@article{Althaus2017, TITLE = {Verification of Linear Hybrid Systems with Large Discrete State Spaces Using Counterexample-guided Abstraction Refinement}, AUTHOR = {Althaus, Ernst and Beber, Bj{\"o}rn and Damm, Werner and Disch, Stefan and Hagemann, Willem and Rakow, Astrid and Scholl, Christoph and Waldmann, Uwe and Wirtz, Boris}, LANGUAGE = {eng}, ISSN = {0167-6423}, DOI = {10.1016/j.scico.2017.04.010}, PUBLISHER = {Elsevier}, ADDRESS = {Amsterdam}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, JOURNAL = {Science of Computer Programming}, VOLUME = {148}, PAGES = {123--160}, }
Endnote
%0 Journal Article %A Althaus, Ernst %A Beber, Bj&#246;rn %A Damm, Werner %A Disch, Stefan %A Hagemann, Willem %A Rakow, Astrid %A Scholl, Christoph %A Waldmann, Uwe %A Wirtz, Boris %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations Automation of Logic, MPI for Informatics, Max Planck Society External Organizations External Organizations Automation of Logic, MPI for Informatics, Max Planck Society External Organizations %T Verification of Linear Hybrid Systems with Large Discrete State Spaces Using Counterexample-guided Abstraction Refinement : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002E-1C23-5 %R 10.1016/j.scico.2017.04.010 %7 2017-05-10 %D 2017 %J Science of Computer Programming %V 148 %& 123 %P 123 - 160 %I Elsevier %C Amsterdam %@ false
Barbosa, H., Blanchette, J. C., Cruanes, S., Ouraoui, D. E., & Fontaine, P. (2017). Language and Proofs for Higher-Order SMT (Work in Progress). Electronic Proceedings in Theoretical Computer Science, 262. doi:10.4204/EPTCS.262.3
(arXiv: 1712.01486)
Abstract
Satisfiability modulo theories (SMT) solvers have throughout the years been able to cope with increasingly expressive formulas, from ground logics to full first-order logic modulo theories. Nevertheless, higher-order logic within SMT is still little explored. One main goal of the Matryoshka project, which started in March 2017, is to extend the reasoning capabilities of SMT solvers and other automatic provers beyond first-order logic. In this preliminary report, we report on an extension of the SMT-LIB language, the standard input format of SMT solvers, to handle higher-order constructs. We also discuss how to augment the proof format of the SMT solver veriT to accommodate these new constructs and the solving techniques they require.
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@article{Barbosa1712.01486, TITLE = {Language and Proofs for Higher-Order {SMT} (Work in Progress)}, AUTHOR = {Barbosa, Haniel and Blanchette, Jasmin Christian and Cruanes, Simon and Ouraoui, Daniel El and Fontaine, Pascal}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1712.01486}, DOI = {10.4204/EPTCS.262.3}, EPRINT = {1712.01486}, EPRINTTYPE = {arXiv}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, ABSTRACT = {Satisfiability modulo theories (SMT) solvers have throughout the years been able to cope with increasingly expressive formulas, from ground logics to full first-order logic modulo theories. Nevertheless, higher-order logic within SMT is still little explored. One main goal of the Matryoshka project, which started in March 2017, is to extend the reasoning capabilities of SMT solvers and other automatic provers beyond first-order logic. In this preliminary report, we report on an extension of the SMT-LIB language, the standard input format of SMT solvers, to handle higher-order constructs. We also discuss how to augment the proof format of the SMT solver veriT to accommodate these new constructs and the solving techniques they require.}, JOURNAL = {Electronic Proceedings in Theoretical Computer Science}, VOLUME = {262}, PAGES = {15--22}, }
Endnote
%0 Journal Article %A Barbosa, Haniel %A Blanchette, Jasmin Christian %A Cruanes, Simon %A Ouraoui, Daniel El %A Fontaine, Pascal %+ External Organizations Automation of Logic, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations %T Language and Proofs for Higher-Order SMT (Work in Progress) : %G eng %U http://hdl.handle.net/21.11116/0000-0000-64DD-7 %R 10.4204/EPTCS.262.3 %U http://arxiv.org/abs/1712.01486 %7 2017 %D 2017 %X Satisfiability modulo theories (SMT) solvers have throughout the years been able to cope with increasingly expressive formulas, from ground logics to full first-order logic modulo theories. Nevertheless, higher-order logic within SMT is still little explored. One main goal of the Matryoshka project, which started in March 2017, is to extend the reasoning capabilities of SMT solvers and other automatic provers beyond first-order logic. In this preliminary report, we report on an extension of the SMT-LIB language, the standard input format of SMT solvers, to handle higher-order constructs. We also discuss how to augment the proof format of the SMT solver veriT to accommodate these new constructs and the solving techniques they require. %K Computer Science, Logic in Computer Science, cs.LO %J Electronic Proceedings in Theoretical Computer Science %O EPTCS %V 262 %& 15 %P 15 - 22
Barbosa, H., Blanchette, J. C., & Fontaine, P. (2017). Scalable Fine-Grained Proofs for Formula Processing. In Automated Deduction -- CADE 26. Gothenburg, Sweden: Springer. doi:10.1007/978-3-319-63046-5_25
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@inproceedings{BarbosaCADE2017, TITLE = {Scalable Fine-Grained Proofs for Formula Processing}, AUTHOR = {Barbosa, Haniel and Blanchette, Jasmin Christian and Fontaine, Pascal}, LANGUAGE = {eng}, ISBN = {978-3-319-63045-8}, DOI = {10.1007/978-3-319-63046-5_25}, PUBLISHER = {Springer}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, BOOKTITLE = {Automated Deduction -- CADE 26}, EDITOR = {de Moura, Leonardo}, PAGES = {398--412}, SERIES = {Lecture Notes in Artificial Intelligence}, VOLUME = {10395}, ADDRESS = {Gothenburg, Sweden}, }
Endnote
%0 Conference Proceedings %A Barbosa, Haniel %A Blanchette, Jasmin Christian %A Fontaine, Pascal %+ External Organizations Automation of Logic, MPI for Informatics, Max Planck Society External Organizations %T Scalable Fine-Grained Proofs for Formula Processing : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002E-0713-5 %R 10.1007/978-3-319-63046-5_25 %D 2017 %B 26th International Conference on Automated Deduction %Z date of event: 2017-08-06 - 2017-08-11 %C Gothenburg, Sweden %B Automated Deduction -- CADE 26 %E de Moura, Leonardo %P 398 - 412 %I Springer %@ 978-3-319-63045-8 %B Lecture Notes in Artificial Intelligence %N 10395
Barkatou, M. A., Jaroschek, M., & Maddah, S. S. (2017). Formal Solutions of Completely Integrable Pfaffian Systems With Normal Crossings. Journal of Symbolic Computation, 81. doi:10.1016/j.jsc.2016.11.018
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@article{Barkatou2017, TITLE = {Formal Solutions of Completely Integrable {Pfaffian} Systems With Normal Crossings}, AUTHOR = {Barkatou, Moulay A. and Jaroschek, Maximilian and Maddah, Suzy S.}, LANGUAGE = {eng}, ISSN = {0747-7171}, DOI = {10.1016/j.jsc.2016.11.018}, PUBLISHER = {Elsevier}, ADDRESS = {Amsterdam}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, JOURNAL = {Journal of Symbolic Computation}, VOLUME = {81}, PAGES = {41--68}, }
Endnote
%0 Journal Article %A Barkatou, Moulay A. %A Jaroschek, Maximilian %A Maddah, Suzy S. %+ External Organizations Automation of Logic, MPI for Informatics, Max Planck Society External Organizations %T Formal Solutions of Completely Integrable Pfaffian Systems With Normal Crossings : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002C-6564-9 %R 10.1016/j.jsc.2016.11.018 %7 2016-11-18 %D 2017 %J Journal of Symbolic Computation %V 81 %& 41 %P 41 - 68 %I Elsevier %C Amsterdam %@ false
Becker, H., Blanchette, J. C., Waldmann, U., & Wand, D. (2017). A Transfinite Knuth–Bendix Order for Lambda-Free Higher-Order Terms. In Automated Deduction -- CADE 26. Gothenburg, Sweden: Springer. doi:10.1007/978-3-319-63046-5_27
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@inproceedings{BeckerCADE2017, TITLE = {A Transfinite {K}nuth&#8211;{B}endix Order for Lambda-Free Higher-Order Terms}, AUTHOR = {Becker, Heiko and Blanchette, Jasmin Christian and Waldmann, Uwe and Wand, Daniel}, LANGUAGE = {eng}, ISBN = {978-3-319-63045-8}, DOI = {10.1007/978-3-319-63046-5_27}, PUBLISHER = {Springer}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, BOOKTITLE = {Automated Deduction -- CADE 26}, EDITOR = {de Moura, Leonardo}, PAGES = {432--453}, SERIES = {Lecture Notes in Artificial Intelligence}, VOLUME = {10395}, ADDRESS = {Gothenburg, Sweden}, }
Endnote
%0 Conference Proceedings %A Becker, Heiko %A Blanchette, Jasmin Christian %A Waldmann, Uwe %A Wand, Daniel %+ External Organizations Automation of Logic, MPI for Informatics, Max Planck Society Automation of Logic, MPI for Informatics, Max Planck Society Automation of Logic, MPI for Informatics, Max Planck Society %T A Transfinite Knuth&#8211;Bendix Order for Lambda-Free Higher-Order Terms : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002E-0711-9 %R 10.1007/978-3-319-63046-5_27 %D 2017 %B 26th International Conference on Automated Deduction %Z date of event: 2017-08-06 - 2017-08-11 %C Gothenburg, Sweden %B Automated Deduction -- CADE 26 %E de Moura, Leonardo %P 432 - 453 %I Springer %@ 978-3-319-63045-8 %B Lecture Notes in Artificial Intelligence %N 10395
Bentkamp, A., Blanchette, J. C., & Klakow, D. (2017). A Formal Proof of the Expressiveness of Deep Learning. In Interactive Theorem Proving (ITP 2017). Brasilia, Brazil: Springer. doi:10.1007/978-3-319-66107-0_4
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@inproceedings{BentkampITP2017, TITLE = {A Formal Proof of the Expressiveness of Deep Learning}, AUTHOR = {Bentkamp, Alexander and Blanchette, Jasmin Christian and Klakow, Dietrich}, LANGUAGE = {eng}, ISBN = {978-3-319-66106-3}, DOI = {10.1007/978-3-319-66107-0_4}, PUBLISHER = {Springer}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, BOOKTITLE = {Interactive Theorem Proving (ITP 2017)}, EDITOR = {Avala-Rinc{\'o}n, Mauricio and Mu{\~n}oz, C{\'e}sar A.}, PAGES = {46--64}, SERIES = {Lecture Notes in Computer Science}, VOLUME = {10499}, ADDRESS = {Brasilia, Brazil}, }
Endnote
%0 Conference Proceedings %A Bentkamp, Alexander %A Blanchette, Jasmin Christian %A Klakow, Dietrich %+ External Organizations Automation of Logic, MPI for Informatics, Max Planck Society External Organizations %T A Formal Proof of the Expressiveness of Deep Learning : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002E-06F8-9 %R 10.1007/978-3-319-66107-0_4 %D 2017 %B 8th Conference on Interactive Theorem Proving %Z date of event: 2017-09-26 - 2017-09-29 %C Brasilia, Brazil %B Interactive Theorem Proving %E Avala-Rinc&#243;n, Mauricio; Mu&#241;oz, C&#233;sar A. %P 46 - 64 %I Springer %@ 978-3-319-66106-3 %B Lecture Notes in Computer Science %N 10499
Biendarra, J., Blanchette, J. C., Bouzy, A., Desharnais, M., Fleury, M., Hölzl, J., … Traytel, D. (2017). Foundational (Co)datatypes and (Co)recursion for Higher-Order Logic. In Frontiers of Combining Systems (FroCoS 2017). Brasília, Brazil: Springer. doi:10.1007/978-3-319-66167-4_1
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@inproceedings{BiendarraFroCoS2017, TITLE = {Foundational (Co)datatypes and (Co)recursion for Higher-Order Logic}, AUTHOR = {Biendarra, Julian and Blanchette, Jasmin Christian and Bouzy, Aymeric and Desharnais, Martin and Fleury, Mathias and H{\"o}lzl, Johannes and Kun{\v c}ar, Ond{\v r}ej and Lochbihler, Andreas and Meier, Fabian and Panny, Lorenz and Popescu, Andrei and Sternagel, Christian and Thiemann, Ren{\'e} and Traytel, Dmitriy}, LANGUAGE = {eng}, ISBN = {978-3-319-66166-7}, DOI = {10.1007/978-3-319-66167-4_1}, PUBLISHER = {Springer}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, BOOKTITLE = {Frontiers of Combining Systems (FroCoS 2017)}, EDITOR = {Dixon, Clare and Finger, Marcelo}, PAGES = {3--21}, SERIES = {Lecture Notes in Artificial Intelligence}, VOLUME = {10483}, ADDRESS = {Bras{\'i}lia, Brazil}, }
Endnote
%0 Conference Proceedings %A Biendarra, Julian %A Blanchette, Jasmin Christian %A Bouzy, Aymeric %A Desharnais, Martin %A Fleury, Mathias %A H&#246;lzl, Johannes %A Kun&#269;ar, Ond&#345;ej %A Lochbihler, Andreas %A Meier, Fabian %A Panny, Lorenz %A Popescu, Andrei %A Sternagel, Christian %A Thiemann, Ren&#233; %A Traytel, Dmitriy %+ External Organizations Automation of Logic, MPI for Informatics, Max Planck Society External Organizations External Organizations Automation of Logic, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations External Organizations External Organizations External Organizations External Organizations External Organizations External Organizations %T Foundational (Co)datatypes and (Co)recursion for Higher-Order Logic : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002E-070E-4 %R 10.1007/978-3-319-66167-4_1 %D 2017 %B 11th International Symposium on Frontiers of Combining Systems %Z date of event: 2017-09-27 - 2017-09-29 %C Bras&#237;lia, Brazil %B Frontiers of Combining Systems %E Dixon, Clare; Finger, Marcelo %P 3 - 21 %I Springer %@ 978-3-319-66166-7 %B Lecture Notes in Artificial Intelligence %N 10483
Blanchette, J. C., Popescu, A., & Traytel, D. (2017a). Abstract Soundness. Archive of Formal Proofs.
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@article{BlanchetteAFP2017, TITLE = {Abstract Soundness}, AUTHOR = {Blanchette, Jasmin Christian and Popescu, Andrei and Traytel, Dmitriy}, LANGUAGE = {eng}, ISSN = {2150-914X}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, JOURNAL = {Archive of Formal Proofs}, }
Endnote
%0 Journal Article %A Blanchette, Jasmin Christian %A Popescu, Andrei %A Traytel, Dmitriy %+ Automation of Logic, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Abstract Soundness : %G eng %U http://hdl.handle.net/21.11116/0000-0000-64A8-2 %7 2017 %D 2017 %J Archive of Formal Proofs %@ false %U https://www.isa-afp.org/browser_info/current/AFP/Abstract_Soundness/document.pdf
Blanchette, J. C., Popescu, A., & Traytel, D. (2017b). Soundness and Completeness Proofs by Coinductive Methods. Journal of Automated Reasoning, 58(1). doi:10.1007/s10817-016-9391-3
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@article{DBLP:journals/jar/BlanchettePT17, TITLE = {Soundness and Completeness Proofs by Coinductive Methods}, AUTHOR = {Blanchette, Jasmin Christian and Popescu, Andrei and Traytel, Dmitriy}, LANGUAGE = {eng}, ISSN = {0168-7433}, DOI = {10.1007/s10817-016-9391-3}, PUBLISHER = {Springer}, ADDRESS = {London}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, JOURNAL = {Journal of Automated Reasoning}, VOLUME = {58}, NUMBER = {1}, PAGES = {149--179}, }
Endnote
%0 Journal Article %A Blanchette, Jasmin Christian %A Popescu, Andrei %A Traytel, Dmitriy %+ Automation of Logic, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Soundness and Completeness Proofs by Coinductive Methods : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002C-3B94-0 %R 10.1007/s10817-016-9391-3 %7 2016-10-18 %D 2017 %J Journal of Automated Reasoning %V 58 %N 1 %& 149 %P 149 - 179 %I Springer %C London %@ false
Blanchette, J. C., Fontaine, P., Schulz, S., & Waldmann, U. (2017). Towards Strong Higher-Order Automation for Fast Interactive Verification. In ARCADE 2017. Gothenburg, Denmark. doi:10.29007/3ngx
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@inproceedings{Blanchette_ARCADE2017, TITLE = {Towards Strong Higher-Order Automation for Fast Interactive Verification}, AUTHOR = {Blanchette, Jasmin Christian and Fontaine, Pascal and Schulz, Stephan and Waldmann, Uwe}, LANGUAGE = {eng}, DOI = {10.29007/3ngx}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {ARCADE 2017}, EDITOR = {Reger, Giles and Traytel, Dmitriy}, PAGES = {16--23}, SERIES = {EPiC Series in Computing}, VOLUME = {51}, ADDRESS = {Gothenburg, Denmark}, }
Endnote
%0 Conference Proceedings %A Blanchette, Jasmin Christian %A Fontaine, Pascal %A Schulz, Stephan %A Waldmann, Uwe %+ Automation of Logic, MPI for Informatics, Max Planck Society External Organizations External Organizations Automation of Logic, MPI for Informatics, Max Planck Society %T Towards Strong Higher-Order Automation for Fast Interactive Verification : %G eng %U http://hdl.handle.net/21.11116/0000-0000-64CF-7 %R 10.29007/3ngx %D 2017 %B 1st International Workshop on Automated Reasoning %Z date of event: 2017-08-06 - 2017-08-06 %C Gothenburg, Denmark %B ARCADE 2017 %E Reger, Giles; Traytel, Dmitriy %P 16 - 23 %B EPiC Series in Computing %N 51
Blanchette, J. C., Fleury, M., & Traytel, D. (2017). Nested Multisets, Hereditary Multisets, and Syntactic Ordinals in Isabelle/HOL. In 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017). Oxford, UK: Schloss Dagstuhl. doi:10.4230/LIPIcs.FSCD.2017.11
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@inproceedings{BlanchetteFSCD2017, TITLE = {Nested Multisets, Hereditary Multisets, and Syntactic Ordinals in {Isabelle}/{HOL}}, AUTHOR = {Blanchette, Jasmin Christian and Fleury, Mathias and Traytel, Dmitriy}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-047-7}, URL = {urn:nbn:de:0030-drops-77155}, DOI = {10.4230/LIPIcs.FSCD.2017.11}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)}, EDITOR = {Miller, Dale}, PAGES = {1--18}, EID = {1}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {84}, ADDRESS = {Oxford, UK}, }
Endnote
%0 Conference Proceedings %A Blanchette, Jasmin Christian %A Fleury, Mathias %A Traytel, Dmitriy %+ Automation of Logic, MPI for Informatics, Max Planck Society Automation of Logic, MPI for Informatics, Max Planck Society External Organizations %T Nested Multisets, Hereditary Multisets, and Syntactic Ordinals in Isabelle/HOL : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002E-06EE-1 %R 10.4230/LIPIcs.FSCD.2017.11 %U urn:nbn:de:0030-drops-77155 %D 2017 %B 2nd International Conference on Formal Structures for Computation and Deduction %Z date of event: 2017-09-03 - 2017-09-09 %C Oxford, UK %B 2nd International Conference on Formal Structures for Computation and Deduction %E Miller, Dale %P 1 - 18 %Z sequence number: 1 %I Schloss Dagstuhl %@ 978-3-95977-047-7 %B Leibniz International Proceedings in Informatics %N 84 %@ false %U http://drops.dagstuhl.de/opus/volltexte/2017/7715/http://drops.dagstuhl.de/doku/urheberrecht1.html
Blanchette, J. C., Fleury, M., & Weidenbach, C. (2017). A Verified SAT Solver Framework with Learn, Forget, Restart, and Incrementality. In Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence (IJCAI 2017). Melbourne, Australia: International Joint Conferences on Artificial Intelligence. doi:10.24963/ijcai.2017/667
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@inproceedings{BlanchetteIJCAI2017, TITLE = {A Verified {SAT} Solver Framework with Learn, Forget, Restart, and Incrementality}, AUTHOR = {Blanchette, Jasmin Christian and Fleury, Mathias and Weidenbach, Christoph}, LANGUAGE = {eng}, ISBN = {978-3-319-40228-4}, DOI = {10.24963/ijcai.2017/667}, PUBLISHER = {International Joint Conferences on Artificial Intelligence}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence (IJCAI 2017)}, EDITOR = {Sierra, Carles}, PAGES = {4786--4790}, ADDRESS = {Melbourne, Australia}, }
Endnote
%0 Conference Proceedings %A Blanchette, Jasmin Christian %A Fleury, Mathias %A Weidenbach, Christoph %+ Automation of Logic, MPI for Informatics, Max Planck Society Automation of Logic, MPI for Informatics, Max Planck Society Automation of Logic, MPI for Informatics, Max Planck Society %T A Verified SAT Solver Framework with Learn, Forget, Restart, and Incrementality : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002E-0702-B %R 10.24963/ijcai.2017/667 %D 2017 %B Twenty-Sixth International Joint Conference on Artificial Intelligence %Z date of event: 2017-08-19 - 2017-08-25 %C Melbourne, Australia %B Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence %E Sierra, Carles %P 4786 - 4790 %I International Joint Conferences on Artificial Intelligence %@ 978-3-319-40228-4
Blanchette, J. C., Waldmann, U., & Wand, D. (2017). A Lambda-Free Higher-Order Recursive Path Order. In Foundations of Software Science and Computation Structures (FoSSaCS 2017). Uppsala, Sweden: Springer. doi:10.1007/978-3-662-54458-7_27
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@inproceedings{BlanchetteFoSSaCS2017, TITLE = {A Lambda-Free Higher-Order Recursive Path Order}, AUTHOR = {Blanchette, Jasmin Christian and Waldmann, Uwe and Wand, Daniel}, LANGUAGE = {eng}, ISBN = {978-3-662-54457-0}, DOI = {10.1007/978-3-662-54458-7_27}, PUBLISHER = {Springer}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, BOOKTITLE = {Foundations of Software Science and Computation Structures (FoSSaCS 2017)}, EDITOR = {Esparza, Javier and Murawski, Andrzej S.}, PAGES = {461--479}, SERIES = {Lecture Notes in Computer Science}, VOLUME = {10203}, ADDRESS = {Uppsala, Sweden}, }
Endnote
%0 Conference Proceedings %A Blanchette, Jasmin Christian %A Waldmann, Uwe %A Wand, Daniel %+ Automation of Logic, MPI for Informatics, Max Planck Society Automation of Logic, MPI for Informatics, Max Planck Society Automation of Logic, MPI for Informatics, Max Planck Society %T A Lambda-Free Higher-Order Recursive Path Order : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002D-91BA-2 %R 10.1007/978-3-662-54458-7_27 %D 2017 %B 20th International Conference on Foundations of Software Science and Computation Structures %Z date of event: 2017-04-24 - 2017-04-27 %C Uppsala, Sweden %B Foundations of Software Science and Computation Structures %E Esparza, Javier; Murawski, Andrzej S. %P 461 - 479 %I Springer %@ 978-3-662-54457-0 %B Lecture Notes in Computer Science %N 10203
Bradford, R., Davenport, J. H., England, M., Errami, H., Gerdt, V., Grigoriev, D., … Weber, A. (2017a). A Case Study on the Parametric Occurrence of Multiple Steady States. In ISSAC’17, International Symposium on Symbolic and Algebraic Computation. Kaiserslautern, Germany: ACM. doi:10.1145/3087604.3087622
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@inproceedings{BradfordISSAC2017, TITLE = {A Case Study on the Parametric Occurrence of Multiple Steady States}, AUTHOR = {Bradford, Russell and Davenport, James H. and England, Matthew and Errami, Hassan and Gerdt, Vladimir and Grigoriev, Dima and Hoyt, Charles and Ko{\v s}ta, Marek and Radulescu, Ovidiu and Sturm, Thomas and Weber, Andreas}, LANGUAGE = {eng}, ISBN = {978-1-4503-5064-8}, DOI = {10.1145/3087604.3087622}, PUBLISHER = {ACM}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, BOOKTITLE = {ISSAC{\textquoteright}17, International Symposium on Symbolic and Algebraic Computation}, PAGES = {45--52}, ADDRESS = {Kaiserslautern, Germany}, }
Endnote
%0 Conference Proceedings %A Bradford, Russell %A Davenport, James H. %A England, Matthew %A Errami, Hassan %A Gerdt, Vladimir %A Grigoriev, Dima %A Hoyt, Charles %A Ko&#353;ta, Marek %A Radulescu, Ovidiu %A Sturm, Thomas %A Weber, Andreas %+ External Organizations External Organizations External Organizations External Organizations External Organizations External Organizations External Organizations External Organizations External Organizations Automation of Logic, MPI for Informatics, Max Planck Society External Organizations %T A Case Study on the Parametric Occurrence of Multiple Steady States : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002E-07B0-1 %R 10.1145/3087604.3087622 %D 2017 %B International Symposium on Symbolic and Algebraic Computation %Z date of event: 2017-07-25 - 2017-07-28 %C Kaiserslautern, Germany %B ISSAC&#8217;17 %P 45 - 52 %I ACM %@ 978-1-4503-5064-8
Bradford, R., Davenport, J. H., England, M., Errami, H., Gerdt, V., Grigoriev, D., … Weber, A. (2017b). A Case Study on the Parametric Occurrence of Multiple Steady States. Retrieved from http://arxiv.org/abs/1704.08997
(arXiv: 1704.08997)
Abstract
We consider the problem of determining multiple steady states for positive real values in models of biological networks. Investigating the potential for these in models of the mitogen-activated protein kinases (MAPK) network has consumed considerable effort using special insights into the structure of corresponding models. Here we apply combinations of symbolic computation methods for mixed equality/inequality systems, specifically virtual substitution, lazy real triangularization and cylindrical algebraic decomposition. We determine multistationarity of an 11-dimensional MAPK network when numeric values are known for all but potentially one parameter. More precisely, our considered model has 11 equations in 11 variables and 19 parameters, 3 of which are of interest for symbolic treatment, and furthermore positivity conditions on all variables and parameters.
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@online{DBLP:journals/corr/BradfordDEEGGHK17, TITLE = {A Case Study on the Parametric Occurrence of Multiple Steady States}, AUTHOR = {Bradford, Russell and Davenport, James H. and England, Matthew and Errami, Hassan and Gerdt, Vladimir and Grigoriev, Dima and Hoyt, Charles and Ko{\v s}ta, Marek and Radulescu, Ovidiu and Sturm, Thomas and Weber, Andreas}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1704.08997}, EPRINT = {1704.08997}, EPRINTTYPE = {arXiv}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, ABSTRACT = {We consider the problem of determining multiple steady states for positive real values in models of biological networks. Investigating the potential for these in models of the mitogen-activated protein kinases (MAPK) network has consumed considerable effort using special insights into the structure of corresponding models. Here we apply combinations of symbolic computation methods for mixed equality/inequality systems, specifically virtual substitution, lazy real triangularization and cylindrical algebraic decomposition. We determine multistationarity of an 11-dimensional MAPK network when numeric values are known for all but potentially one parameter. More precisely, our considered model has 11 equations in 11 variables and 19 parameters, 3 of which are of interest for symbolic treatment, and furthermore positivity conditions on all variables and parameters.}, }
Endnote
%0 Report %A Bradford, Russell %A Davenport, James H. %A England, Matthew %A Errami, Hassan %A Gerdt, Vladimir %A Grigoriev, Dima %A Hoyt, Charles %A Ko&#353;ta, Marek %A Radulescu, Ovidiu %A Sturm, Thomas %A Weber, Andreas %+ External Organizations External Organizations External Organizations External Organizations External Organizations External Organizations External Organizations External Organizations External Organizations Automation of Logic, MPI for Informatics, Max Planck Society External Organizations %T A Case Study on the Parametric Occurrence of Multiple Steady States : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002D-91D0-E %U http://arxiv.org/abs/1704.08997 %D 2017 %X We consider the problem of determining multiple steady states for positive real values in models of biological networks. Investigating the potential for these in models of the mitogen-activated protein kinases (MAPK) network has consumed considerable effort using special insights into the structure of corresponding models. Here we apply combinations of symbolic computation methods for mixed equality/inequality systems, specifically virtual substitution, lazy real triangularization and cylindrical algebraic decomposition. We determine multistationarity of an 11-dimensional MAPK network when numeric values are known for all but potentially one parameter. More precisely, our considered model has 11 equations in 11 variables and 19 parameters, 3 of which are of interest for symbolic treatment, and furthermore positivity conditions on all variables and parameters. %K Computer Science, Symbolic Computation, cs.SC
Bromberger, M., & Weidenbach, C. (2017). New Techniques for Linear Arithmetic: Cubes and Equalities. Formal Methods in System Design, 51(3). doi:10.1007/s10703-017-0278-7
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@article{Bromberger2017, TITLE = {New Techniques for Linear Arithmetic: {C}ubes and Equalities}, AUTHOR = {Bromberger, Martin and Weidenbach, Christoph}, LANGUAGE = {eng}, ISSN = {0925-9856}, DOI = {10.1007/s10703-017-0278-7}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, JOURNAL = {Formal Methods in System Design}, VOLUME = {51}, NUMBER = {3}, PAGES = {433--461}, }
Endnote
%0 Journal Article %A Bromberger, Martin %A Weidenbach, Christoph %+ Automation of Logic, MPI for Informatics, Max Planck Society Automation of Logic, MPI for Informatics, Max Planck Society %T New Techniques for Linear Arithmetic: Cubes and Equalities : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002E-260E-C %R 10.1007/s10703-017-0278-7 %7 2017 %D 2017 %J Formal Methods in System Design %V 51 %N 3 %& 433 %P 433 - 461 %I Springer %C Berlin %@ false
Demri, S., Kapur, D., & Weidenbach, C. (2017). Preface -Special Issue of Selected Extended Papers of IJCAR 2014. Journal of Automated Reasoning, 58(1). doi:10.1007/s10817-016-9394-0
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@article{DBLP:journals/jar/DemriKW17, TITLE = {Preface -- Special Issue of Selected Extended Papers of {IJCAR} 2014}, AUTHOR = {Demri, St{\'e}phane and Kapur, Deepak and Weidenbach, Christoph}, LANGUAGE = {eng}, ISSN = {0168-7433}, DOI = {10.1007/s10817-016-9394-0}, PUBLISHER = {D. Reidel Pub. Co.}, ADDRESS = {Dordrecht, Holland}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, JOURNAL = {Journal of Automated Reasoning}, VOLUME = {58}, NUMBER = {1}, PAGES = {1--2}, }
Endnote
%0 Journal Article %A Demri, St&#233;phane %A Kapur, Deepak %A Weidenbach, Christoph %+ External Organizations External Organizations Automation of Logic, MPI for Informatics, Max Planck Society %T Preface -Special Issue of Selected Extended Papers of IJCAR 2014 : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002C-4CD1-C %R 10.1007/s10817-016-9394-0 %7 2016 %D 2017 %J Journal of Automated Reasoning %V 58 %N 1 %& 1 %P 1 - 2 %I D. Reidel Pub. Co. %C Dordrecht, Holland %@ false
Echenim, M., Peltier, N., & Tourret, S. (2017). Prime Implicate Generation in Equational Logic. Journal of Artificial Intelligence Research, 60. doi:10.1613/jair.5481
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@article{Echenim2017, TITLE = {Prime Implicate Generation in Equational Logic}, AUTHOR = {Echenim, Mnacho and Peltier, Nicolas and Tourret, Sophie}, LANGUAGE = {eng}, ISSN = {1076-9757}, DOI = {10.1613/jair.5481}, PUBLISHER = {AI Access Foundation}, ADDRESS = {S.l.}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, JOURNAL = {Journal of Artificial Intelligence Research}, VOLUME = {60}, PAGES = {827--880}, }
Endnote
%0 Journal Article %A Echenim, Mnacho %A Peltier, Nicolas %A Tourret, Sophie %+ External Organizations External Organizations Automation of Logic, MPI for Informatics, Max Planck Society %T Prime Implicate Generation in Equational Logic : %G eng %U http://hdl.handle.net/21.11116/0000-0000-C8DF-4 %R 10.1613/jair.5481 %7 2017 %D 2017 %J Journal of Artificial Intelligence Research %V 60 %& 827 %P 827 - 880 %I AI Access Foundation %C S.l. %@ false
England, M., Errami, H., Grigoriev, D., Radulescu, O., Sturm, T., & Weber, A. (2017a). Symbolic Versus Numerical Computation and Visualization of Parameter Regions for Multistationarity of Biological Networks. In Computer Algebra in Scientific Computing. Beijing, China: Springer. doi:10.1007/978-3-319-66320-3_8
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@inproceedings{EnglandCASC2017, TITLE = {Symbolic Versus Numerical Computation and Visualization of Parameter Regions for Multistationarity of Biological Networks}, AUTHOR = {England, Matthew and Errami, Hassan and Grigoriev, Dima and Radulescu, Ovidiu and Sturm, Thomas and Weber, Andreas}, LANGUAGE = {eng}, ISBN = {978-3-319-66319-7}, DOI = {10.1007/978-3-319-66320-3_8}, PUBLISHER = {Springer}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, BOOKTITLE = {Computer Algebra in Scientific Computing}, EDITOR = {Gerdt, Vladimir P. and Koepf, Wolfram and Seiler, Werner M. and Vorozhtsov, Evgenii V.}, PAGES = {93--108}, SERIES = {Lecture Notes in Computer Science}, VOLUME = {10490}, ADDRESS = {Beijing, China}, }
Endnote
%0 Conference Proceedings %A England, Matthew %A Errami, Hassan %A Grigoriev, Dima %A Radulescu, Ovidiu %A Sturm, Thomas %A Weber, Andreas %+ External Organizations External Organizations External Organizations External Organizations Automation of Logic, MPI for Informatics, Max Planck Society External Organizations %T Symbolic Versus Numerical Computation and Visualization of Parameter Regions for Multistationarity of Biological Networks : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002E-07A0-5 %R 10.1007/978-3-319-66320-3_8 %D 2017 %B 19th International Workshop on Computer Algebra in Scientific Computing %Z date of event: 2017-09-18 - 2017-09-22 %C Beijing, China %B Computer Algebra in Scientific Computing %E Gerdt, Vladimir P.; Koepf, Wolfram; Seiler, Werner M.; Vorozhtsov, Evgenii V. %P 93 - 108 %I Springer %@ 978-3-319-66319-7 %B Lecture Notes in Computer Science %N 10490
England, M., Errami, H., Grigoriev, D., Radulescu, O., Sturm, T., & Weber, A. (2017b). Symbolic Versus Numerical Computation and Visualization of Parameter Regions for Multistationarity of Biological Networks. Retrieved from http://arxiv.org/abs/1706.08794
(arXiv: 1706.08794)
Abstract
We investigate models of the mitogenactivated protein kinases (MAPK) network, with the aim of determining where in parameter space there exist multiple positive steady states. We build on recent progress which combines various symbolic computation methods for mixed systems of equalities and inequalities. We demonstrate that those techniques benefit tremendously from a newly implemented graph theoretical symbolic preprocessing method. We compare computation times and quality of results of numerical continuation methods with our symbolic approach before and after the application of our preprocessing.
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@online{DBLP:journals/corr/EnglandEGR0017, TITLE = {Symbolic Versus Numerical Computation and Visualization of Parameter Regions for Multistationarity of Biological Networks}, AUTHOR = {England, Matthew and Errami, Hassan and Grigoriev, Dima and Radulescu, Ovidiu and Sturm, Thomas and Weber, Andreas}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1706.08794}, EPRINT = {1706.08794}, EPRINTTYPE = {arXiv}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, ABSTRACT = {We investigate models of the mitogenactivated protein kinases (MAPK) network, with the aim of determining where in parameter space there exist multiple positive steady states. We build on recent progress which combines various symbolic computation methods for mixed systems of equalities and inequalities. We demonstrate that those techniques benefit tremendously from a newly implemented graph theoretical symbolic preprocessing method. We compare computation times and quality of results of numerical continuation methods with our symbolic approach before and after the application of our preprocessing.}, }
Endnote
%0 Report %A England, Matthew %A Errami, Hassan %A Grigoriev, Dima %A Radulescu, Ovidiu %A Sturm, Thomas %A Weber, Andreas %+ External Organizations External Organizations External Organizations External Organizations Automation of Logic, MPI for Informatics, Max Planck Society External Organizations %T Symbolic Versus Numerical Computation and Visualization of Parameter Regions for Multistationarity of Biological Networks : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002D-91C9-F %U http://arxiv.org/abs/1706.08794 %D 2017 %X We investigate models of the mitogenactivated protein kinases (MAPK) network, with the aim of determining where in parameter space there exist multiple positive steady states. We build on recent progress which combines various symbolic computation methods for mixed systems of equalities and inequalities. We demonstrate that those techniques benefit tremendously from a newly implemented graph theoretical symbolic preprocessing method. We compare computation times and quality of results of numerical continuation methods with our symbolic approach before and after the application of our preprocessing. %K Computer Science, Symbolic Computation, cs.SC
Fontaine, P., Ogawa, M., Sturm, T., & Vu, X. T. (2017a). Subtropical Satisfiability. In Frontiers of Combining Systems (FroCoS 2017). Brasília, Brazil: Springer. doi:10.1007/978-3-319-66167-4_11
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@inproceedings{FontaineFroCoS2017, TITLE = {Subtropical Satisfiability}, AUTHOR = {Fontaine, Pascal and Ogawa, Mizuhito and Sturm, Thomas and Vu, Xuan Tung}, LANGUAGE = {eng}, ISBN = {978-3-319-66166-7}, DOI = {10.1007/978-3-319-66167-4_11}, PUBLISHER = {Springer}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, BOOKTITLE = {Frontiers of Combining Systems (FroCoS 2017)}, EDITOR = {Dixon, Clare and Finger, Marcelo}, PAGES = {189--206}, SERIES = {Lecture Notes in Artificial Intelligence}, VOLUME = {10483}, ADDRESS = {Bras{\'i}lia, Brazil}, }
Endnote
%0 Conference Proceedings %A Fontaine, Pascal %A Ogawa, Mizuhito %A Sturm, Thomas %A Vu, Xuan Tung %+ External Organizations External Organizations Automation of Logic, MPI for Informatics, Max Planck Society External Organizations %T Subtropical Satisfiability : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002E-07A7-8 %R 10.1007/978-3-319-66167-4_11 %D 2017 %B 11th International Symposium on Frontiers of Combining Systems %Z date of event: 2017-09-27 - 2017-09-29 %C Bras&#237;lia, Brazil %B Frontiers of Combining Systems %E Dixon, Clare; Finger, Marcelo %P 189 - 206 %I Springer %@ 978-3-319-66166-7 %B Lecture Notes in Artificial Intelligence %N 10483
Fontaine, P., Ogawa, M., Sturm, T., & Vu, X. T. (2017b). Subtropical Satisfiability. Retrieved from http://arxiv.org/abs/1706.09236
(arXiv: 1706.09236)
Abstract
Quantifier-free nonlinear arithmetic (QF_NRA) appears in many applications of satisfiability modulo theories solving (SMT). Accordingly, efficient reasoning for corresponding constraints in SMT theory solvers is highly relevant. We propose a new incomplete but efficient and terminating method to identify satisfiable instances. The method is derived from the subtropical method recently introduced in the context of symbolic computation for computing real zeros of single very large multivariate polynomials. Our method takes as input conjunctions of strict polynomial inequalities, which represent more than 40% of the QF_NRA section of the SMT-LIB library of benchmarks. The method takes an abstraction of polynomials as exponent vectors over the natural numbers tagged with the signs of the corresponding coefficients. It then uses, in turn, SMT to solve linear problems over the reals to heuristically find suitable points that translate back to satisfying points for the original problem. Systematic experiments on the SMT-LIB demonstrate that our method is not a sufficiently strong decision procedure by itself but a valuable heuristic to use within a portfolio of techniques.
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@online{DBLP:journals/corr/FontaineO0V17, TITLE = {Subtropical Satisfiability}, AUTHOR = {Fontaine, Pascal and Ogawa, Mizuhito and Sturm, Thomas and Vu, Xuan Tung}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1706.09236}, EPRINT = {1706.09236}, EPRINTTYPE = {arXiv}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, ABSTRACT = {Quantifier-free nonlinear arithmetic (QF_NRA) appears in many applications of satisfiability modulo theories solving (SMT). Accordingly, efficient reasoning for corresponding constraints in SMT theory solvers is highly relevant. We propose a new incomplete but efficient and terminating method to identify satisfiable instances. The method is derived from the subtropical method recently introduced in the context of symbolic computation for computing real zeros of single very large multivariate polynomials. Our method takes as input conjunctions of strict polynomial inequalities, which represent more than 40% of the QF_NRA section of the SMT-LIB library of benchmarks. The method takes an abstraction of polynomials as exponent vectors over the natural numbers tagged with the signs of the corresponding coefficients. It then uses, in turn, SMT to solve linear problems over the reals to heuristically find suitable points that translate back to satisfying points for the original problem. Systematic experiments on the SMT-LIB demonstrate that our method is not a sufficiently strong decision procedure by itself but a valuable heuristic to use within a portfolio of techniques.}, }
Endnote
%0 Report %A Fontaine, Pascal %A Ogawa, Mizuhito %A Sturm, Thomas %A Vu, Xuan Tung %+ External Organizations External Organizations Automation of Logic, MPI for Informatics, Max Planck Society External Organizations %T Subtropical Satisfiability : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002D-91C2-E %U http://arxiv.org/abs/1706.09236 %D 2017 %X Quantifier-free nonlinear arithmetic (QF_NRA) appears in many applications of satisfiability modulo theories solving (SMT). Accordingly, efficient reasoning for corresponding constraints in SMT theory solvers is highly relevant. We propose a new incomplete but efficient and terminating method to identify satisfiable instances. The method is derived from the subtropical method recently introduced in the context of symbolic computation for computing real zeros of single very large multivariate polynomials. Our method takes as input conjunctions of strict polynomial inequalities, which represent more than 40% of the QF_NRA section of the SMT-LIB library of benchmarks. The method takes an abstraction of polynomials as exponent vectors over the natural numbers tagged with the signs of the corresponding coefficients. It then uses, in turn, SMT to solve linear problems over the reals to heuristically find suitable points that translate back to satisfying points for the original problem. Systematic experiments on the SMT-LIB demonstrate that our method is not a sufficiently strong decision procedure by itself but a valuable heuristic to use within a portfolio of techniques. %K Computer Science, Logic in Computer Science, cs.LO
Horbach, M., Voigt, M., & Weidenbach, C. (2017a). On the Combination of the Bernays-Schönfinkel-Ramsey Fragment with Simple Linear Integer Arithmetic. In Automated Deduction -- CADE 26. Gothenburg, Sweden: Springer. doi:10.1007/978-3-319-63046-5_6
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@inproceedings{HorbachCADE2017, TITLE = {On the Combination of the {B}ernays-{S}ch&#246;nfinkel-{R}amsey Fragment with Simple Linear Integer Arithmetic}, AUTHOR = {Horbach, Matthias and Voigt, Marco and Weidenbach, Christoph}, LANGUAGE = {eng}, ISBN = {978-3-319-63045-8}, DOI = {10.1007/978-3-319-63046-5_6}, PUBLISHER = {Springer}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, BOOKTITLE = {Automated Deduction -- CADE 26}, EDITOR = {de Moura, Leonardo}, PAGES = {77--94}, SERIES = {Lecture Notes in Artificial Intelligence}, VOLUME = {10395}, ADDRESS = {Gothenburg, Sweden}, }
Endnote
%0 Conference Proceedings %A Horbach, Matthias %A Voigt, Marco %A Weidenbach, Christoph %+ Automation of Logic, MPI for Informatics, Max Planck Society Automation of Logic, MPI for Informatics, Max Planck Society Automation of Logic, MPI for Informatics, Max Planck Society %T On the Combination of the Bernays-Sch&#246;nfinkel-Ramsey Fragment with Simple Linear Integer Arithmetic : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002D-FB27-F %R 10.1007/978-3-319-63046-5_6 %D 2017 %B 26th International Conference on Automated Deduction %Z date of event: 2017-08-06 - 2017-08-11 %C Gothenburg, Sweden %B Automated Deduction -- CADE 26 %E de Moura, Leonardo %P 77 - 94 %I Springer %@ 978-3-319-63045-8 %B Lecture Notes in Artificial Intelligence %N 10395
Horbach, M., Voigt, M., & Weidenbach, C. (2017b). On the Combination of the Bernays-Schönfinkel-Ramsey Fragment with Simple Linear Integer Arithmetic. Retrieved from http://arxiv.org/abs/1705.08792
(arXiv: 1705.08792)
Abstract
In general, first-order predicate logic extended with linear integer arithmetic is undecidable. We show that the Bernays-Sch\"onfinkel-Ramsey fragment ($\exists^* \forall^*$-sentences) extended with a restricted form of linear integer arithmetic is decidable via finite ground instantiation. The identified ground instances can be employed to restrict the search space of existing automated reasoning procedures considerably, e.g., when reasoning about quantified properties of array data structures formalized in Bradley, Manna, and Sipma's array property fragment. Typically, decision procedures for the array property fragment are based on an exhaustive instantiation of universally quantified array indices with all the ground index terms that occur in the formula at hand. Our results reveal that one can get along with significantly fewer instances.
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@online{HorbachArXiv2017, TITLE = {On the Combination of the Bernays-Sch{\"o}nfinkel-Ramsey Fragment with Simple Linear Integer Arithmetic}, AUTHOR = {Horbach, Matthias and Voigt, Marco and Weidenbach, Christoph}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1705.08792}, EPRINT = {1705.08792}, EPRINTTYPE = {arXiv}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, ABSTRACT = {In general, first-order predicate logic extended with linear integer arithmetic is undecidable. We show that the Bernays-Sch\"onfinkel-Ramsey fragment ($\exists^* \forall^*$-sentences) extended with a restricted form of linear integer arithmetic is decidable via finite ground instantiation. The identified ground instances can be employed to restrict the search space of existing automated reasoning procedures considerably, e.g., when reasoning about quantified properties of array data structures formalized in Bradley, Manna, and Sipma's array property fragment. Typically, decision procedures for the array property fragment are based on an exhaustive instantiation of universally quantified array indices with all the ground index terms that occur in the formula at hand. Our results reveal that one can get along with significantly fewer instances.}, }
Endnote
%0 Report %A Horbach, Matthias %A Voigt, Marco %A Weidenbach, Christoph %+ Automation of Logic, MPI for Informatics, Max Planck Society Automation of Logic, MPI for Informatics, Max Planck Society Automation of Logic, MPI for Informatics, Max Planck Society %T On the Combination of the Bernays-Sch&#246;nfinkel-Ramsey Fragment with Simple Linear Integer Arithmetic : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002D-8140-2 %U http://arxiv.org/abs/1705.08792 %D 2017 %X In general, first-order predicate logic extended with linear integer arithmetic is undecidable. We show that the Bernays-Sch\"onfinkel-Ramsey fragment ($\exists^* \forall^*$-sentences) extended with a restricted form of linear integer arithmetic is decidable via finite ground instantiation. The identified ground instances can be employed to restrict the search space of existing automated reasoning procedures considerably, e.g., when reasoning about quantified properties of array data structures formalized in Bradley, Manna, and Sipma's array property fragment. Typically, decision procedures for the array property fragment are based on an exhaustive instantiation of universally quantified array indices with all the ground index terms that occur in the formula at hand. Our results reveal that one can get along with significantly fewer instances. %K Computer Science, Logic in Computer Science, cs.LO
Horbach, M., Voigt, M., & Weidenbach, C. (2017c). The Universal Fragment of Presburger Arithmetic with Unary Uninterpreted Predicates is Undecidable. Retrieved from http://arxiv.org/abs/1703.01212
(arXiv: 1703.01212)
Abstract
The first-order theory of addition over the natural numbers, known as Presburger arithmetic, is decidable in double exponential time. Adding an uninterpreted unary predicate to the language leads to an undecidable theory. We sharpen the known boundary between decidable and undecidable in that we show that the purely universal fragment of the extended theory is already undecidable. Our proof is based on a reduction of the halting problem for two-counter machines to unsatisfiability of sentences in the extended language of Presburger arithmetic that does not use existential quantification. On the other hand, we argue that a single $\forall\exists$ quantifier alternation turns the set of satisfiable sentences of the extended language into a $\Sigma^1_1$-complete set. Some of the mentioned results can be transfered to the realm of linear arithmetic over the ordered real numbers. This concerns the undecidability of the purely universal fragment and the $\Sigma^1_1$-hardness for sentences with at least one quantifier alternation. Finally, we discuss the relevance of our results to verification. In particular, we derive undecidability results for quantified fragments of separation logic, the theory of arrays, and combinations of the theory of equality over uninterpreted functions with restricted forms of integer arithmetic. In certain cases our results even imply the absence of sound and complete deductive calculi.
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@online{VoigtHorbachWeidenbacharXiv2017, TITLE = {The Universal Fragment of Presburger Arithmetic with Unary Uninterpreted Predicates is Undecidable}, AUTHOR = {Horbach, Matthias and Voigt, Marco and Weidenbach, Christoph}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1703.01212}, EPRINT = {1703.01212}, EPRINTTYPE = {arXiv}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, ABSTRACT = {The first-order theory of addition over the natural numbers, known as Presburger arithmetic, is decidable in double exponential time. Adding an uninterpreted unary predicate to the language leads to an undecidable theory. We sharpen the known boundary between decidable and undecidable in that we show that the purely universal fragment of the extended theory is already undecidable. Our proof is based on a reduction of the halting problem for two-counter machines to unsatisfiability of sentences in the extended language of Presburger arithmetic that does not use existential quantification. On the other hand, we argue that a single $\forall\exists$ quantifier alternation turns the set of satisfiable sentences of the extended language into a $\Sigma^1_1$-complete set. Some of the mentioned results can be transfered to the realm of linear arithmetic over the ordered real numbers. This concerns the undecidability of the purely universal fragment and the $\Sigma^1_1$-hardness for sentences with at least one quantifier alternation. Finally, we discuss the relevance of our results to verification. In particular, we derive undecidability results for quantified fragments of separation logic, the theory of arrays, and combinations of the theory of equality over uninterpreted functions with restricted forms of integer arithmetic. In certain cases our results even imply the absence of sound and complete deductive calculi.}, }
Endnote
%0 Report %A Horbach, Matthias %A Voigt, Marco %A Weidenbach, Christoph %+ Automation of Logic, MPI for Informatics, Max Planck Society Automation of Logic, MPI for Informatics, Max Planck Society Automation of Logic, MPI for Informatics, Max Planck Society %T The Universal Fragment of Presburger Arithmetic with Unary Uninterpreted Predicates is Undecidable : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002C-A5E7-D %U http://arxiv.org/abs/1703.01212 %D 2017 %X The first-order theory of addition over the natural numbers, known as Presburger arithmetic, is decidable in double exponential time. Adding an uninterpreted unary predicate to the language leads to an undecidable theory. We sharpen the known boundary between decidable and undecidable in that we show that the purely universal fragment of the extended theory is already undecidable. Our proof is based on a reduction of the halting problem for two-counter machines to unsatisfiability of sentences in the extended language of Presburger arithmetic that does not use existential quantification. On the other hand, we argue that a single $\forall\exists$ quantifier alternation turns the set of satisfiable sentences of the extended language into a $\Sigma^1_1$-complete set. Some of the mentioned results can be transfered to the realm of linear arithmetic over the ordered real numbers. This concerns the undecidability of the purely universal fragment and the $\Sigma^1_1$-hardness for sentences with at least one quantifier alternation. Finally, we discuss the relevance of our results to verification. In particular, we derive undecidability results for quantified fragments of separation logic, the theory of arrays, and combinations of the theory of equality over uninterpreted functions with restricted forms of integer arithmetic. In certain cases our results even imply the absence of sound and complete deductive calculi. %K Computer Science, Logic in Computer Science, cs.LO
Lamotte-Schubert, M., & Weidenbach, C. (2017). BDI: A New Decidable Clause Class. Journal of Logic and Computation, 27(2). doi:10.1093/logcom/exu074
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@article{Lamotte-SchubertWeidenbach13a, TITLE = {{BDI}: A New Decidable Clause Class}, AUTHOR = {Lamotte-Schubert, Manuel and Weidenbach, Christoph}, LANGUAGE = {eng}, ISSN = {0955-792X}, DOI = {10.1093/logcom/exu074}, PUBLISHER = {Oxford University Press}, ADDRESS = {Oxford}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, JOURNAL = {Journal of Logic and Computation}, VOLUME = {27}, NUMBER = {2}, PAGES = {441--468}, }
Endnote
%0 Journal Article %A Lamotte-Schubert, Manuel %A Weidenbach, Christoph %+ Automation of Logic, MPI for Informatics, Max Planck Society Automation of Logic, MPI for Informatics, Max Planck Society %T BDI: A New Decidable Clause Class : %G eng %U http://hdl.handle.net/11858/00-001M-0000-0024-C365-F %R 10.1093/logcom/exu074 %7 2014-12-08 %D 2017 %J Journal of Logic and Computation %V 27 %N 2 %& 441 %P 441 - 468 %I Oxford University Press %C Oxford %@ false %U https://hal.inria.fr/hal-01098084
Reynolds, A., & Blanchette, J. C. (2017). A Decision Procedure for (Co)datatypes in SMT Solvers. Journal of Automated Reasoning, 58(3). doi:10.1007/s10817-016-9372-6
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@article{DBLP:journals/jar/ReynoldsB17, TITLE = {A Decision Procedure for (Co)datatypes in {SMT} Solvers}, AUTHOR = {Reynolds, Andrew and Blanchette, Jasmin Christian}, LANGUAGE = {eng}, ISSN = {0168-7433}, DOI = {10.1007/s10817-016-9372-6}, PUBLISHER = {Springer}, ADDRESS = {New York, NY}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, JOURNAL = {Journal of Automated Reasoning}, EDITOR = {Kambhampati, Subbarao}, VOLUME = {58}, NUMBER = {3}, PAGES = {341--362}, }
Endnote
%0 Journal Article %A Reynolds, Andrew %A Blanchette, Jasmin Christian %+ External Organizations Automation of Logic, MPI for Informatics, Max Planck Society %T A Decision Procedure for (Co)datatypes in SMT Solvers : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002C-80D4-C %R 10.1007/s10817-016-9372-6 %7 2017 %D 2017 %J Journal of Automated Reasoning %V 58 %N 3 %& 341 %P 341 - 362 %I Springer %C New York, NY %@ false
Sturm, T. (2017). A Survey of Some Methods for Real Quantifier Elimination, Decision, and Satisfiability and Their Applications. Mathematics in Computer Science, 11(3-4). doi:10.1007/s11786-017-0319-z
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@article{Sturm2017, TITLE = {A Survey of Some Methods for Real Quantifier Elimination, Decision, and Satisfiability and Their Applications}, AUTHOR = {Sturm, Thomas}, LANGUAGE = {eng}, DOI = {10.1007/s11786-017-0319-z}, PUBLISHER = {Springer}, ADDRESS = {New York, NY}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, JOURNAL = {Mathematics in Computer Science}, VOLUME = {11}, NUMBER = {3-4}, PAGES = {483--502}, }
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%0 Journal Article %A Sturm, Thomas %+ Automation of Logic, MPI for Informatics, Max Planck Society %T A Survey of Some Methods for Real Quantifier Elimination, Decision, and Satisfiability and Their Applications : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002C-A3B5-B %R 10.1007/s11786-017-0319-z %7 2017 %D 2017 %J Mathematics in Computer Science %V 11 %N 3-4 %& 483 %P 483 - 502 %I Springer %C New York, NY
Tang, C. H. (2017). Logics for Rule-based Configuration Systems. Universität des Saarlandes, Saarbrücken. Retrieved from urn:nbn:de:bsz:291-scidok-69639
Abstract
Rule-based configuration systems are being successfully used in industry, such as DOPLER at Siemens. Those systems make complex domain knowledge available to users and let them derive valid, customized products out of large sets of components. However, maintenance of such systems remains a challenge. Formal models are a prerequisite for the use of automated methods of analysis. This thesis deals with the formalization of rule-based configuration. We develop two logics whose transition semantics are suited for expressing the way systems like DOPLER operate. This is due to the existence of two types of transitions, namely user and rule transitions, and a fixpoint mechanism that determines their dynamic relationship. The first logic, PIDL, models propositional systems, while the second logic, PIDL+, additionally considers arithmetic constraints. They allow the formulation and automated verification of relevant properties of rule- based configuration systems.
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@phdthesis{Tangphd2017, TITLE = {Logics for Rule-based Configuration Systems}, AUTHOR = {Tang, Ching Hoo}, LANGUAGE = {eng}, URL = {urn:nbn:de:bsz:291-scidok-69639}, SCHOOL = {Universit{\"a}t des Saarlandes}, ADDRESS = {Saarbr{\"u}cken}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, ABSTRACT = {Rule-based configuration systems are being successfully used in industry, such as DOPLER at Siemens. Those systems make complex domain knowledge available to users and let them derive valid, customized products out of large sets of components. However, maintenance of such systems remains a challenge. Formal models are a prerequisite for the use of automated methods of analysis. This thesis deals with the formalization of rule-based configuration. We develop two logics whose transition semantics are suited for expressing the way systems like DOPLER operate. This is due to the existence of two types of transitions, namely user and rule transitions, and a fixpoint mechanism that determines their dynamic relationship. The first logic, PIDL, models propositional systems, while the second logic, PIDL+, additionally considers arithmetic constraints. They allow the formulation and automated verification of relevant properties of rule- based configuration systems.}, }
Endnote
%0 Thesis %A Tang, Ching Hoo %Y Weidenbach, Christoph %A referee: Herzig, Andreas %+ Automation of Logic, MPI for Informatics, Max Planck Society International Max Planck Research School, MPI for Informatics, Max Planck Society Automation of Logic, MPI for Informatics, Max Planck Society External Organizations %T Logics for Rule-based Configuration Systems : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002E-0871-7 %U urn:nbn:de:bsz:291-scidok-69639 %I Universit&#228;t des Saarlandes %C Saarbr&#252;cken %D 2017 %P X, 123 p. %V phd %9 phd %X Rule-based configuration systems are being successfully used in industry, such as DOPLER at Siemens. Those systems make complex domain knowledge available to users and let them derive valid, customized products out of large sets of components. However, maintenance of such systems remains a challenge. Formal models are a prerequisite for the use of automated methods of analysis. This thesis deals with the formalization of rule-based configuration. We develop two logics whose transition semantics are suited for expressing the way systems like DOPLER operate. This is due to the existence of two types of transitions, namely user and rule transitions, and a fixpoint mechanism that determines their dynamic relationship. The first logic, PIDL, models propositional systems, while the second logic, PIDL+, additionally considers arithmetic constraints. They allow the formulation and automated verification of relevant properties of rule- based configuration systems. %U http://scidok.sulb.uni-saarland.de/doku/lic_ohne_pod.php?la=dehttp://scidok.sulb.uni-saarland.de/volltexte/2017/6963/
Teucke, A., & Weidenbach, C. (2017a). Decidability of the Monadic Shallow Linear First-Order Fragment with Straight Dismatching Constraints. In Automated Deduction -- CADE 26. Gothenburg, Sweden: Springer. doi:10.1007/978-3-319-63046-5_13
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@inproceedings{TeuckeCADE2017, TITLE = {Decidability of the Monadic Shallow Linear First-Order Fragment with Straight Dismatching Constraints}, AUTHOR = {Teucke, Andreas and Weidenbach, Christoph}, LANGUAGE = {eng}, ISBN = {978-3-319-63045-8}, DOI = {10.1007/978-3-319-63046-5_13}, PUBLISHER = {Springer}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, BOOKTITLE = {Automated Deduction -- CADE 26}, EDITOR = {de Moura, Leonardo}, PAGES = {202--219}, SERIES = {Lecture Notes in Artificial Intelligence}, VOLUME = {10395}, ADDRESS = {Gothenburg, Sweden}, }
Endnote
%0 Conference Proceedings %A Teucke, Andreas %A Weidenbach, Christoph %+ Automation of Logic, MPI for Informatics, Max Planck Society Automation of Logic, MPI for Informatics, Max Planck Society %T Decidability of the Monadic Shallow Linear First-Order Fragment with Straight Dismatching Constraints : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002D-FB2A-9 %R 10.1007/978-3-319-63046-5_13 %D 2017 %B 26th International Conference on Automated Deduction %Z date of event: 2017-08-06 - 2017-08-11 %C Gothenburg, Sweden %B Automated Deduction -- CADE 26 %E de Moura, Leonardo %P 202 - 219 %I Springer %@ 978-3-319-63045-8 %B Lecture Notes in Artificial Intelligence %N 10395
Teucke, A., & Weidenbach, C. (2017b). Decidability of the Monadic Shallow Linear First-Order Fragment with Straight Dismatching Constraints. Retrieved from http://arxiv.org/abs/1703.02837
(arXiv: 1703.02837)
Abstract
The monadic shallow linear Horn fragment is well-known to be decidable and has many application, e.g., in security protocol analysis, tree automata, or abstraction refinement. It was a long standing open problem how to extend the fragment to the non-Horn case, preserving decidability, that would, e.g., enable to express non-determinism in protocols. We prove decidability of the non-Horn monadic shallow linear fragment via ordered resolution further extended with dismatching constraints and discuss some applications of the new decidable fragment.
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@online{TeuckearXiv2017, TITLE = {Decidability of the Monadic Shallow Linear First-Order Fragment with Straight Dismatching Constraints}, AUTHOR = {Teucke, Andreas and Weidenbach, Christoph}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1703.02837}, EPRINT = {1703.02837}, EPRINTTYPE = {arXiv}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, ABSTRACT = {The monadic shallow linear Horn fragment is well-known to be decidable and has many application, e.g., in security protocol analysis, tree automata, or abstraction refinement. It was a long standing open problem how to extend the fragment to the non-Horn case, preserving decidability, that would, e.g., enable to express non-determinism in protocols. We prove decidability of the non-Horn monadic shallow linear fragment via ordered resolution further extended with dismatching constraints and discuss some applications of the new decidable fragment.}, }
Endnote
%0 Report %A Teucke, Andreas %A Weidenbach, Christoph %+ Automation of Logic, MPI for Informatics, Max Planck Society Automation of Logic, MPI for Informatics, Max Planck Society %T Decidability of the Monadic Shallow Linear First-Order Fragment with Straight Dismatching Constraints : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002C-A213-1 %U http://arxiv.org/abs/1703.02837 %D 2017 %X The monadic shallow linear Horn fragment is well-known to be decidable and has many application, e.g., in security protocol analysis, tree automata, or abstraction refinement. It was a long standing open problem how to extend the fragment to the non-Horn case, preserving decidability, that would, e.g., enable to express non-determinism in protocols. We prove decidability of the non-Horn monadic shallow linear fragment via ordered resolution further extended with dismatching constraints and discuss some applications of the new decidable fragment. %K Computer Science, Logic in Computer Science, cs.LO
Voigt, M. (2017a). A Fine-Grained Hierarchy of Hard Problems in the Separated Fragment. In 32nd Annual ACM-IEEE Symposium on Logic in Computer Science (LICS 2017). Reykjavik, Island: ACM. doi:10.1109/LICS.2017.8005094
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@inproceedings{VoigtLICS2017, TITLE = {A Fine-Grained Hierarchy of Hard Problems in the Separated Fragment}, AUTHOR = {Voigt, Marco}, LANGUAGE = {eng}, ISBN = {978-1-5090-3019-4}, DOI = {10.1109/LICS.2017.8005094}, PUBLISHER = {ACM}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, BOOKTITLE = {32nd Annual ACM-IEEE Symposium on Logic in Computer Science (LICS 2017)}, PAGES = {1--12}, ADDRESS = {Reykjavik, Island}, }
Endnote
%0 Conference Proceedings %A Voigt, Marco %+ Automation of Logic, MPI for Informatics, Max Planck Society %T A Fine-Grained Hierarchy of Hard Problems in the Separated Fragment : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002C-EFA6-4 %R 10.1109/LICS.2017.8005094 %D 2017 %B 32nd Annual ACM-IEEE Symposium on Logic in Computer Science %Z date of event: 2017-06-20 - 2017-06-23 %C Reykjavik, Island %B 32nd Annual ACM-IEEE Symposium on Logic in Computer Science %P 1 - 12 %I ACM %@ 978-1-5090-3019-4
Voigt, M. (2017b). A Fine-Grained Hierarchy of Hard Problems in the Separated Fragment. Retrieved from http://arxiv.org/abs/1704.02145
(arXiv: 1704.02145)
Abstract
Recently, the separated fragment (SF) has been introduced and proved to be decidable. Its defining principle is that universally and existentially quantified variables may not occur together in atoms. The known upper bound on the time required to decide SF's satisfiability problem is formulated in terms of quantifier alternations: Given an SF sentence $\exists \vec{z} \forall \vec{x}_1 \exists \vec{y}_1 \ldots \forall \vec{x}_n \exists \vec{y}_n . \psi$ in which $\psi$ is quantifier free, satisfiability can be decided in nondeterministic $n$-fold exponential time. In the present paper, we conduct a more fine-grained analysis of the complexity of SF-satisfiability. We derive an upper and a lower bound in terms of the degree of interaction of existential variables (short: degree)}---a novel measure of how many separate existential quantifier blocks in a sentence are connected via joint occurrences of variables in atoms. Our main result is the $k$-NEXPTIME-completeness of the satisfiability problem for the set $SF_{\leq k}$ of all SF sentences that have degree $k$ or smaller. Consequently, we show that SF-satisfiability is non-elementary in general, since SF is defined without restrictions on the degree. Beyond trivial lower bounds, nothing has been known about the hardness of SF-satisfiability so far.
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@online{VoigtLICS2017ArxivFullPaper, TITLE = {A Fine-Grained Hierarchy of Hard Problems in the Separated Fragment}, AUTHOR = {Voigt, Marco}, URL = {http://arxiv.org/abs/1704.02145}, EPRINT = {1704.02145}, EPRINTTYPE = {arXiv}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, ABSTRACT = {Recently, the separated fragment (SF) has been introduced and proved to be decidable. Its defining principle is that universally and existentially quantified variables may not occur together in atoms. The known upper bound on the time required to decide SF's satisfiability problem is formulated in terms of quantifier alternations: Given an SF sentence $\exists \vec{z} \forall \vec{x}_1 \exists \vec{y}_1 \ldots \forall \vec{x}_n \exists \vec{y}_n . \psi$ in which $\psi$ is quantifier free, satisfiability can be decided in nondeterministic $n$-fold exponential time. In the present paper, we conduct a more fine-grained analysis of the complexity of SF-satisfiability. We derive an upper and a lower bound in terms of the degree of interaction of existential variables (short: degree)}---a novel measure of how many separate existential quantifier blocks in a sentence are connected via joint occurrences of variables in atoms. Our main result is the $k$-NEXPTIME-completeness of the satisfiability problem for the set $SF_{\leq k}$ of all SF sentences that have degree $k$ or smaller. Consequently, we show that SF-satisfiability is non-elementary in general, since SF is defined without restrictions on the degree. Beyond trivial lower bounds, nothing has been known about the hardness of SF-satisfiability so far.}, }
Endnote
%0 Report %A Voigt, Marco %+ Automation of Logic, MPI for Informatics, Max Planck Society %T A Fine-Grained Hierarchy of Hard Problems in the Separated Fragment : %U http://hdl.handle.net/11858/00-001M-0000-002C-EFA0-0 %U http://arxiv.org/abs/1704.02145 %D 2017 %X Recently, the separated fragment (SF) has been introduced and proved to be decidable. Its defining principle is that universally and existentially quantified variables may not occur together in atoms. The known upper bound on the time required to decide SF's satisfiability problem is formulated in terms of quantifier alternations: Given an SF sentence $\exists \vec{z} \forall \vec{x}_1 \exists \vec{y}_1 \ldots \forall \vec{x}_n \exists \vec{y}_n . \psi$ in which $\psi$ is quantifier free, satisfiability can be decided in nondeterministic $n$-fold exponential time. In the present paper, we conduct a more fine-grained analysis of the complexity of SF-satisfiability. We derive an upper and a lower bound in terms of the degree of interaction of existential variables (short: degree)}---a novel measure of how many separate existential quantifier blocks in a sentence are connected via joint occurrences of variables in atoms. Our main result is the $k$-NEXPTIME-completeness of the satisfiability problem for the set $SF_{\leq k}$ of all SF sentences that have degree $k$ or smaller. Consequently, we show that SF-satisfiability is non-elementary in general, since SF is defined without restrictions on the degree. Beyond trivial lower bounds, nothing has been known about the hardness of SF-satisfiability so far. %K Computer Science, Logic in Computer Science, cs.LO
Wand, D. (2017). Superposition: Types and Induction. Universität des Saarlandes, Saarbrücken. Retrieved from urn:nbn:de:bsz:291-scidok-69522
Abstract
Proof assistants are becoming widespread for formalization of theories both in computer science and mathematics. They provide rich logics with powerful type systems and machine-checked proofs which increase the confidence in the correctness in complicated and detailed proofs. However, they incur a significant overhead compared to pen-and-paper proofs. This thesis describes work on bridging the gap between high-order proof assistants and first-order automated theorem provers by extending the capabilities of the automated theorem provers to provide features usually found in proof assistants. My first contribution is the development and implementation of a first-order superposition calculus with a polymorphic type system that supports type classes and the accompanying refutational completeness proof for that calculus. The inclusion of the type system into the superposition calculus and solvers completely removes the type encoding overhead when encoding problems from many proof assistants. My second contribution is the development of SupInd, an extension of the typed superposition calculus that supports data types and structural induction over those data types. It includes heuristics that guide the induction and conjecture strengthening techniques, which can be applied independently of the underlying calculus. I have implemented the contributions in a tool called Pirate. The evaluations of both contributions show promising results.
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@phdthesis{wandphd2017, TITLE = {Superposition: Types and Induction}, AUTHOR = {Wand, Daniel}, LANGUAGE = {eng}, URL = {urn:nbn:de:bsz:291-scidok-69522}, SCHOOL = {Universit{\"a}t des Saarlandes}, ADDRESS = {Saarbr{\"u}cken}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, ABSTRACT = {Proof assistants are becoming widespread for formalization of theories both in computer science and mathematics. They provide rich logics with powerful type systems and machine-checked proofs which increase the confidence in the correctness in complicated and detailed proofs. However, they incur a significant overhead compared to pen-and-paper proofs. This thesis describes work on bridging the gap between high-order proof assistants and first-order automated theorem provers by extending the capabilities of the automated theorem provers to provide features usually found in proof assistants. My first contribution is the development and implementation of a first-order superposition calculus with a polymorphic type system that supports type classes and the accompanying refutational completeness proof for that calculus. The inclusion of the type system into the superposition calculus and solvers completely removes the type encoding overhead when encoding problems from many proof assistants. My second contribution is the development of SupInd, an extension of the typed superposition calculus that supports data types and structural induction over those data types. It includes heuristics that guide the induction and conjecture strengthening techniques, which can be applied independently of the underlying calculus. I have implemented the contributions in a tool called Pirate. The evaluations of both contributions show promising results.}, }
Endnote
%0 Thesis %A Wand, Daniel %Y Weidenbach, Christoph %A referee: Blanchette, Jasmin Christian %A referee: Sutcliffe, Geoff %+ Automation of Logic, MPI for Informatics, Max Planck Society International Max Planck Research School, MPI for Informatics, Max Planck Society Automation of Logic, MPI for Informatics, Max Planck Society Automation of Logic, MPI for Informatics, Max Planck Society Automation of Logic, MPI for Informatics, Max Planck Society %T Superposition: Types and Induction : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002D-E99C-5 %U urn:nbn:de:bsz:291-scidok-69522 %I Universit&#228;t des Saarlandes %C Saarbr&#252;cken %D 2017 %P x, 167 p. %V phd %9 phd %X Proof assistants are becoming widespread for formalization of theories both in computer science and mathematics. They provide rich logics with powerful type systems and machine-checked proofs which increase the confidence in the correctness in complicated and detailed proofs. However, they incur a significant overhead compared to pen-and-paper proofs. This thesis describes work on bridging the gap between high-order proof assistants and first-order automated theorem provers by extending the capabilities of the automated theorem provers to provide features usually found in proof assistants. My first contribution is the development and implementation of a first-order superposition calculus with a polymorphic type system that supports type classes and the accompanying refutational completeness proof for that calculus. The inclusion of the type system into the superposition calculus and solvers completely removes the type encoding overhead when encoding problems from many proof assistants. My second contribution is the development of SupInd, an extension of the typed superposition calculus that supports data types and structural induction over those data types. It includes heuristics that guide the induction and conjecture strengthening techniques, which can be applied independently of the underlying calculus. I have implemented the contributions in a tool called Pirate. The evaluations of both contributions show promising results. %U http://scidok.sulb.uni-saarland.de/volltexte/2017/6952/http://scidok.sulb.uni-saarland.de/doku/lic_ohne_pod.php?la=de
Weidenbach, C. (2017). Do Portfolio Solvers Harm? In ARCADE 2017. Gothenburg, Denmark. doi:10.29007/vpxm
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@inproceedings{Weidenbach_ARCADE2017, TITLE = {Do Portfolio Solvers Harm?}, AUTHOR = {Weidenbach, Christoph}, LANGUAGE = {eng}, DOI = {10.29007/vpxm}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {ARCADE 2017}, EDITOR = {Reger, Giles and Traytel, Dmitriy}, PAGES = {76--81}, SERIES = {EPiC Series in Computing}, VOLUME = {51}, ADDRESS = {Gothenburg, Denmark}, }
Endnote
%0 Conference Proceedings %A Weidenbach, Christoph %+ Automation of Logic, MPI for Informatics, Max Planck Society %T Do Portfolio Solvers Harm? : %G eng %U http://hdl.handle.net/21.11116/0000-0000-3C43-2 %R 10.29007/vpxm %D 2017 %B 1st International Workshop on Automated Reasoning %Z date of event: 2017-08-06 - 2017-08-06 %C Gothenburg, Denmark %B ARCADE 2017 %E Reger, Giles; Traytel, Dmitriy %P 76 - 81 %B EPiC Series in Computing %N 51