Work

Deciding the weak definability of Büchi definable tree languages

Year: 2013

Type: article

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.

Source: DROPS (Schloss Dagstuhl – Leibniz Center for Informatics)

Parent work: LIPIcs, Volume 23, CSL'13, Complete Volume

DOI: 10.4230/lipics.csl.2013.215

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

Institutions: Délégation Paris 7, Université Paris Diderot, Université Paris Cité, RWTH Aachen University, University of Oxford

Language: English

Topic: semigroups and automata theory

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funder: European Commission