Deciding the weak definability of Büchi definable tree languages
Thomas Colcombet,Denis Kuperberg,Christof Löding,Michael Vanden Boom +3 more
- Vol. 23, pp 215-230
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TLDR
The main result is that given a Buchi automaton, it is decidable whether the language is weakly definable.Abstract:
Weakly definable languages of infinite trees are an expressive subclass of regular tree languages definable in terms of weak monadic second-order logic, or equivalently weak alternating automata. Our main result is that given a Buchi automaton, it is decidable whether the language is weakly definable. We also show that given a parity automaton, it is decidable whether the language is recognizable by a nondeterministic co-Buchi automaton.
The decidability proofs build on recent results about cost automata over infinite trees. These automata use counters to define functions from infinite trees to the natural numbers extended with infinity. We reduce to testing whether the functions defined by certain "quasi-weak" cost automata are bounded by a finite value.read more
Citations
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Proceedings ArticleDOI
Rabin-Mostowski Index Problem: A Step beyond Deterministic Automata
TL;DR: This work investigates a wider class of regular languages, recognisable by so-called game automata, which can be seen as the closure of deterministic ones under complementation and composition and shows that it is decidable whether a given regular language can be recognised by a game automaton.
Proceedings ArticleDOI
Two-way cost automata and cost logics over infinite trees
TL;DR: This work considers cost functions over infinite trees defined by an extension of weak monadic second-order logic with a new fixed-point-like operator, and shows this logic to be decidable, improving previously known decidability results for cost logics over infinite Trees.
Proceedings ArticleDOI
Deciding the Topological Complexity of Büchi Languages.
TL;DR: It is shown that a language of Buchi automata on infinite binary trees is either Borel and WMSO-definable, or Sigma_1^1-complete and not W MSO-Definable; moreover it can be algorithmically decided which of the two cases holds.
Proceedings ArticleDOI
On the Way to Alternating Weak Automata
Udi Boker,Karoliina Lehtinen +1 more
TL;DR: It is shown that Alternating parity word automata can be turned into alternating weak automata of quasi-polynomial (rather than exponential) size, which corresponds to a weak version of the canonical game languages known to be strict for the Mostowski - Rabin index hierarchy.
Proceedings ArticleDOI
Alternating weak automata from universal trees
TL;DR: Any slightly better translation from alternating parity automata on infinite words to alternating weak automata would lead to algorithms for solving parity games that are asymptotically faster in the worst case than the current state of the art, and hence would yield a significant breakthrough.
References
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Book ChapterDOI
Languages, automata, and logic
TL;DR: The subject of this chapter is the study of formal languages (mostly languages recognizable by finite automata) in the framework of mathematical logic.
Journal ArticleDOI
Decidability of second-order theories and automata on infinite trees
TL;DR: In this article, it was shown that the second-order theory of countable linearly ordered sets is decidable, and that the theory of automata on infinite trees is also decidable.
Proceedings ArticleDOI
Trees, automata, and games
Yuri Gurevich,Leo Harrington +1 more
TL;DR: This work gives here an alternative and transparent proof of Rabin's result on tree automata, which is based on ideas of his predecessors and especially those of B- and-uuml;chi-&-mdash;.
Journal ArticleDOI
Simulating alternating tree automata by nondeterministic automata: new results and new proofs of the theorems of Rabin, McNaughton and Safra
David E. Muller,Paul E. Schupp +1 more
TL;DR: A unified proof of the theorems of Rabin, McNaughton and Safra is given and a simple axiomatic framework for uniformizing strategies is given.