New decidable upper bound of the second level in the Straubing-Therien concatenation hierarchy of star-free languages
Jorge Almeida (1), Ondrej Klima (2) (3)
(1) Departamento de Matemática [Porto]
(2) Department of Mathematics and Statistics [Btno]
(3) Department of Mathematics and Statistics [Masaryk University, Brno]
Abstract
In a recent paper we gave a counterexample to a longstanding conjecture concerning the characterization of regular languages of level 2 in the Straubing-Therien concatenation hierarchy of star-free languages. In that paper a new upper bound for the corresponding pseudovariety of monoids was implicitly given. In this paper we show that it is decidable whether a given monoid belongs to the new upper bound. We also prove that this new upper bound is incomparable with the previous upper bound.
