• Moulay A. Barkatou, Maximilian Jaroschek, and Suzy S. Maddah, "Formal Solutions of Completely Integrable Pfaffian Systems With Normal Crossings," Journal of Symbolic Computation 81, 41-68 (2017).  
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    Moulay A. Barkatou, Maximilian Jaroschek, and Suzy S. Maddah, "Formal Solutions of Completely Integrable Pfaffian Systems With Normal Crossings," Journal of Symbolic Computation 81, 41-68 (2017).
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  • Jasmin Christian Blanchette, Andrei Popescu, and Dmitriy Traytel, "Soundness and Completeness Proofs by Coinductive Methods," Journal of Automated Reasoning 58 (1), 149-179 (2017).  
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    Jasmin Christian Blanchette, Andrei Popescu, and Dmitriy Traytel, "Soundness and Completeness Proofs by Coinductive Methods," Journal of Automated Reasoning 58 (1), 149-179 (2017).
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  • Jasmin Christian Blanchette, Uwe Waldmann, and Daniel Wand, "A Lambda-Free Higher-Order Recursive Path Order", in Foundations of Software Science and Computation Structures, edited by Javier Esparza and Andrzej S. Murawski (Springer, Berlin, 2017), pp. 461-479.  
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    Jasmin Christian Blanchette, Uwe Waldmann, and Daniel Wand, "A Lambda-Free Higher-Order Recursive Path Order", in Foundations of Software Science and Computation Structures, edited by Javier Esparza and Andrzej S. Murawski (Springer, Berlin, 2017), pp. 461-479.
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  • Russell Bradford, James H. Davenport, Matthew England, Hassan Errami, Vladimir Gerdt, Dima Grigoriev, Charles Hoyt, Marek Košta, Ovidiu Radulescu, Thomas Sturm, and Andreas Weber, "A Case Study on the Parametric Occurrence of Multiple Steady States", (2017), pp. 9 p.  
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    Russell Bradford, James H. Davenport, Matthew England, Hassan Errami, Vladimir Gerdt, Dima Grigoriev, Charles Hoyt, Marek Košta, Ovidiu Radulescu, Thomas Sturm, and Andreas Weber, "A Case Study on the Parametric Occurrence of Multiple Steady States", (2017), pp. 9 p.
    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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  • Stéphane Demri, Deepak Kapur, and Christoph Weidenbach, "Preface -Special Issue of Selected Extended Papers of IJCAR 2014," Journal of Automated Reasoning 58 (1), 1-2 (2017).  
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    Stéphane Demri, Deepak Kapur, and Christoph Weidenbach, "Preface -Special Issue of Selected Extended Papers of IJCAR 2014," Journal of Automated Reasoning 58 (1), 1-2 (2017).
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  • Matthew England, Hassan Errami, Dima Grigoriev, Ovidiu Radulescu, Thomas Sturm, and Andreas Weber, "Symbolic Versus Numerical Computation and Visualization of Parameter Regions for Multistationarity of Biological Networks", (2017), pp. 15 p.  
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    Matthew England, Hassan Errami, Dima Grigoriev, Ovidiu Radulescu, Thomas Sturm, and Andreas Weber, "Symbolic Versus Numerical Computation and Visualization of Parameter Regions for Multistationarity of Biological Networks", (2017), pp. 15 p.
    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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  • Pascal Fontaine, Mizuhito Ogawa, Thomas Sturm, and Xuan Tung Vu, "Subtropical Satisfiability", (2017), pp. 17 p.  
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    Pascal Fontaine, Mizuhito Ogawa, Thomas Sturm, and Xuan Tung Vu, "Subtropical Satisfiability", (2017), pp. 17 p.
    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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  • Matthias Horbach, Marco Voigt, and Christoph Weidenbach, "The Universal Fragment of Presburger Arithmetic with Unary Uninterpreted Predicates is Undecidable", (2017), pp. 22 p.  
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    Matthias Horbach, Marco Voigt, and Christoph Weidenbach, "The Universal Fragment of Presburger Arithmetic with Unary Uninterpreted Predicates is Undecidable", (2017), pp. 22 p.
    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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  • Matthias Horbach, Marco Voigt, and Christoph Weidenbach, "On the Combination of the Bernays-Schönfinkel-Ramsey Fragment with Simple Linear Integer Arithmetic", (2017), pp. 29 p.  
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    Matthias Horbach, Marco Voigt, and Christoph Weidenbach, "On the Combination of the Bernays-Schönfinkel-Ramsey Fragment with Simple Linear Integer Arithmetic", (2017), pp. 29 p.
    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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  • Manuel Lamotte-Schubert and Christoph Weidenbach, "BDI: A New Decidable Clause Class," Journal of Logic and Computation 27 (2), 441-468 (2017).  
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    Manuel Lamotte-Schubert and Christoph Weidenbach, "BDI: A New Decidable Clause Class," Journal of Logic and Computation 27 (2), 441-468 (2017).
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  • Andrew Reynolds and Jasmin Christian Blanchette, "A Decision Procedure for (Co)datatypes in SMT Solvers," Journal of Automated Reasoning 58 (3), 341-362 (2017).  
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    Andrew Reynolds and Jasmin Christian Blanchette, "A Decision Procedure for (Co)datatypes in SMT Solvers," Journal of Automated Reasoning 58 (3), 341-362 (2017).
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  • Andreas Teucke and Christoph Weidenbach, "Decidability of the Monadic Shallow Linear First-Order Fragment with Straight Dismatching Constraints", (2017), pp. 28 p.  
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    Andreas Teucke and Christoph Weidenbach, "Decidability of the Monadic Shallow Linear First-Order Fragment with Straight Dismatching Constraints", (2017), pp. 28 p.
    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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  • Marco Voigt, "A Fine-Grained Hierarchy of Hard Problems in the Separated Fragment", (2017), pp. 38 p.  
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    Marco Voigt, "A Fine-Grained Hierarchy of Hard Problems in the Separated Fragment", (2017), pp. 38 p.
    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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