Abstract
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.
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Behle, C., Krebs, A., Reifferscheid, S. (2011). Typed Monoids – An Eilenberg-Like Theorem for Non Regular Languages. In: Winkler, F. (eds) Algebraic Informatics. CAI 2011. Lecture Notes in Computer Science, vol 6742. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21493-6_6
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DOI: https://doi.org/10.1007/978-3-642-21493-6_6
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