Deciding the Borel Complexity of Regular Tree Languages

Facchini, Alessandro; Michalewski, Henryk

doi:10.1007/978-3-319-08019-2_17

Cited by 2 publications

(1 citation statement)

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“…Concerning the decidability of the topological complexity of regular languages, it has been shown recently by M. Bojanczyk and T. Place in [BP12] that one can decide whether a regular language accepted by a given tree automaton is a boolean combination of open sets. This result has been extended by A. Facchini and H. Michalewski in [FM14], where the authors prove that one can decide whether a regular tree language is in the class ∆ 0 2 . The question is still open for the other levels of the Borel hierarchy, or whether a regular tree language is Borel, analytic, coanalytic, or in any class Γ present in this paper.…”

Section: Discussionmentioning

confidence: 84%

An upper bound on the complexity of recognizable tree languages

Finkel

Lecomte

Simonnet

2015

RAIRO-Theor. Inf. Appl.

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The third author noticed in his 1992 PhD Thesis [Sim92] that every regular tree language of infinite trees is in a class (D n (Σ 0 2 )) for some natural number n ≥ 1, where is the game quantifier. We first give a detailed exposition of this result. Next, using an embedding of the Wadge hierarchy of non self-dual Borel subsets of the Cantor space 2 ω into the class ∆ 1 2 , and the notions of Wadge degree and Veblen function, we argue that this upper bound on the topological complexity of regular tree languages is much better than the usual ∆ 1 2 .

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Section: Discussionmentioning

confidence: 84%