• 1 Departamento de Matemática [Porto]
• 2 Department of Mathematics and Statistics [Btno]
• 3 Department of Mathematics and Statistics [Masaryk University, Brno]

special issue dedicated to the second edition of the conference AutoMathA: from Mathematics to Applications

[en]
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.