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

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Authors	ALMEIDA Jorge KLÍMA Ondřej
Year of publication	2010
Type	Article in Periodical
Magazine / Source	Discrete Mathematics & Theoretical Computer Science
MU Faculty or unit	Faculty of Science
Citation
Field	General mathematics
Keywords	formal languages; regular languages; concatenation hierarchies; level two; star-free languages
Description	In a recent paper we gave a counterexample to a longstanding conjecture concerning the characterization of regular languages of level 2 in the Straubing-Thérien 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.
Related projects:	Institute for Theoretical Computer Science Mathematical structures and their physical applications Algebraic Methods in Automata and Formal Language Theory II