An Upper Bound on the Complexity of Recognizable Tree Languages - Archive ouverte HAL
Journal Articles RAIRO - Theoretical Informatics and Applications (RAIRO: ITA) Year : 2015

An Upper Bound on the Complexity of Recognizable Tree Languages

Abstract

The third author noticed in his 1992 PhD Thesis [Sim92] that every regular tree language of infinite trees is in a class $\Game (D_n({\bf\Sigma}^0_2))$ for some natural number $n\geq 1$, where $\Game$ 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 $2^\omega$ into the class ${\bf\Delta}^1_2$, 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 ${\bf\Delta}^1_2$.
Fichier principal
Vignette du fichier
Upper-Bound-aout-2014-3-v2-2.pdf (273.83 Ko) Télécharger le fichier
Origin Files produced by the author(s)
Loading...

Dates and versions

hal-01128609 , version 1 (10-03-2015)

Identifiers

Cite

Olivier Finkel, Dominique Lecomte, Pierre Simonnet. An Upper Bound on the Complexity of Recognizable Tree Languages. RAIRO - Theoretical Informatics and Applications (RAIRO: ITA), 2015, 49 (2), pp.121-137. ⟨hal-01128609⟩
271 View
117 Download

Altmetric

Share

More