@INPROCEEDINGS{GanzingerJacquemardVeanes-98-asian, AUTHOR = {Ganzinger, H. and Jacquemard, F. and Veanes, M.}, TITLE = {Rigid Reachability}, BOOKTITLE = {Proc.\ ASIAN'98}, PUBLISHER = {Springer-Verlag}, SERIES = {Lecture Notes in Computer Science}, ADDRESS = {Berlin}, VOLUME = {1538}, PAGES ={4--21}, YEAR = {1998}, ABSTRACT = { We show that rigid reachability, the non-symmetric form of rigid $E$-unification, is undecidable already in the case of a single constraint. From this we infer the undecidability of a new rather restricted kind of second-order unification. We also show that certain decidable subclasses of the problem which are \PTIME-complete in the equational case become \EXPTIME-complete when symmetry is absent. By applying automata-theoretic methods, simultaneous monadic rigid reachability with ground rules is shown to be in \EXPTIME. }, URL = {\hgURL{~hg/pca.html#98ASIAN}} }