Deciding the weak definability of Büchi definable tree languages

Colcombet, Thomas; Kuperberg, Denis; Löding, Christof; Vanden Boom, Michael

doi:10.4230/LIPIcs.CSL.2013.215

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Deciding the weak definability of Büchi definable tree languages

Authors Thomas Colcombet, Denis Kuperberg, Christof Löding, Michael Vanden Boom

Part of: Volume: Computer Science Logic 2013 (CSL 2013)
Part of: Series: Leibniz International Proceedings in Informatics (LIPIcs)
Part of: Conference: Computer Science Logic (CSL)
License: Creative Commons Attribution 3.0 Unported license
Publication Date: 2013-09-02

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Document Identifiers

DOI: 10.4230/LIPIcs.CSL.2013.215
URN: urn:nbn:de:0030-drops-41998

Subject Classification

Keywords

Tree automata
weak definability
decidability
cost automata
boundedness

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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 Büchi 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-Büchi 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.

Cite As Get BibTex

Thomas Colcombet, Denis Kuperberg, Christof Löding, and Michael Vanden Boom. Deciding the weak definability of Büchi definable tree languages. In Computer Science Logic 2013 (CSL 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 23, pp. 215-230, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013) https://doi.org/10.4230/LIPIcs.CSL.2013.215

Author Details

Thomas Colcombet

Denis Kuperberg

Christof Löding

Michael Vanden Boom

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