New decidable upper bound of the second level in the Straubing-Therien concatenation hierarchy of star-free languages

Jorge Almeida 1 Ondrej Klima 2
1 Departamento de Matemática [Porto]
2 Department of Mathematics and Statistics [Btno]
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.
Keywords : formal languages regular languages concatenation hierarchies level two star-free languages
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Discrete Mathematics and Theoretical Computer Science, DMTCS, 2010, 12 (4), pp.41-58
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Jorge Almeida, Ondrej Klima. New decidable upper bound of the second level in the Straubing-Therien concatenation hierarchy of star-free languages. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2010, 12 (4), pp.41-58. 〈hal-00990443〉

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