Automata on Infinite Trees with Equality and Disequality Constraints Between Siblings

This article is inspired by two works from the early 90s. The first one is by Bogaert and Tison who considered a model of automata on finite ranked trees where one can check equality and disequality constraints between direct subtrees: they proved that this class of automata is closed under Boolean...

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Veröffentlicht in:Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science S. 227 - 236
Hauptverfasser: Carayol, Arnaud, Löding, Christof, Serre, Olivier
Format: Tagungsbericht
Sprache:Englisch
Veröffentlicht: New York, NY, USA ACM 05.07.2016
Schriftenreihe:ACM Conferences
Schlagworte:
Theory of computation
Theory of computation > Formal languages and automata theory
Theory of computation > Logic
Automata on infinite trees
Automata with equality and disequality constraints
Emptiness problem
Finiteness problem
ISBN:9781450343916, 1450343910
Online-Zugang:Volltext
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Beschreibung
Zusammenfassung:This article is inspired by two works from the early 90s. The first one is by Bogaert and Tison who considered a model of automata on finite ranked trees where one can check equality and disequality constraints between direct subtrees: they proved that this class of automata is closed under Boolean operations and that both the emptiness and the finiteness problem of the accepted language are decidable. The second one is by Niwinski who showed that one can compute the cardinality of any ω-regular language of infinite trees. Here, we generalise the model of automata of Tison and Bogaert to the setting of infinite binary trees. Roughly speaking we consider parity tree automata where some transitions are guarded and can be used only when the two direct sub-trees of the current node are equal/disequal. We show that the resulting class of languages encompasses the one of ω-regular languages of infinite trees while sharing most of its closure properties, in particular it is a Boolean algebra. Our main technical contribution is then to prove that it also enjoys a decidable cardinality problem. In particular, this implies the decidability of the emptiness problem.
ISBN:9781450343916
1450343910
DOI:10.1145/2933575.2934504