Based on different concepts to obtain a finer notion of language recognition via finite monoids we develop an algebraic structure called typed monoid. This leads to an algebraic description of regular and non regular languages. We obtain for each language a unique minimal recognizing typed monoid, the typed syntactic monoid. We prove an Eilenberg-like theorem for varieties of typed monoids as well as a similar correspondence for classes of languages with weaker closure properties than varieties. © 2011 Springer-Verlag.
CITATION STYLE
Behle, C., Krebs, A., & Reifferscheid, S. (2011). Typed monoids - An Eilenberg-like theorem for non regular languages. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6742 LNCS, pp. 97–114). https://doi.org/10.1007/978-3-642-21493-6_6
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