The Recognizability Problem for Tree Automata with Comparisons between Brothers

Authors:
Bruno Bogaert;Franck Seynhaeve;Sophie Tison
Affiliations:
-;-;-
Venue:
FoSSaCS '99 Proceedings of the Second International Conference on Foundations of Software Science and Computation Structure, Held as Part of the European Joint Conferences on the Theory and Practice of Software, ETAPS'99
Year:
1999

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Abstract

Several extensions of tree automata have been defined, in order to take in account non-linearity in terms. Roughly, these automata allow equality or disequality constraints between subterms. They have been used to get decision results, e.g. in term rewriting. One natural question arises when we consider a language recognized by such an automaton: is this language recognizable, i.e. are the constraints necessary? Here we study this problem in the class REC# corresponding to comparisons between brothers and we prove its decidability. It gives e.g. a decision procedure for testing whether the image by a quasi-alphabetic homomorphism of a recognizable tree language is recognizable.