Tree automata with equality constraints modulo equational theories

abstract: This paper presents new classes of tree automata combining automata with equality test and automata modulo equational theories. We believe that this class has a good potential for application in e.g. software verification. These tree automata are obtained by extending the standard Horn clause representations with equational conditions and rewrite systems. We show in particular that a generalized membership problem (extending the emptiness problem) is decidable by proving that the saturation of tree automata presentations with suitable paramodulation strategies terminates. Alternatively our results can be viewed as new decidable classes of first-order formula.

Recommended citation: Florent Jacquemard, Michaël Rusinowitch, and Laurent Vigneron, "Tree automata with equality constraints modulo equational theories" In Proceedings of the 3rd International Joint Conference on Automated Reasoning (IJCAR’06), volume 4130 of Lecture Notes in Artificial Intelligence, pages 557–571, Springer-Verlag, 2006.