Tree Automata with Global Constraints

Authors:
Emmanuel Filiot;Jean-Marc Talbot;Sophie Tison
Affiliations:
INRIA Lille - Nord Europe, Mostrare Project, University of Lille 1 (LIFL, UMR 8022 of CNRS),;University of Provence (LIF, UMR 6166 of CNRS), Marseille,;INRIA Lille - Nord Europe, Mostrare Project, University of Lille 1 (LIFL, UMR 8022 of CNRS),
Venue:
DLT '08 Proceedings of the 12th international conference on Developments in Language Theory
Year:
2008

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Abstract

A tree automaton with global tree equality and disequality constraints, TAGED for short, is an automaton on trees which allows to test (dis)equalities between subtrees which may be arbitrarily faraway. In particular, it is equipped with an (dis)equality relation on states, so that whenever two subtrees tand t茂戮驴 evaluate (in an accepting run) to two states which are in the (dis)equality relation, they must be (dis)equal. We study several properties of TAGEDs, and prove decidability of emptiness of several classes. We give two applications of TAGEDs: decidability of an extension of Monadic Second Order Logic with tree isomorphism tests and of unification with membership constraints. These results significantly improve the results of [10].