Christoph Behle

Typed monoids: an Eilenberg-like theorem for non regular languages

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.

Non-solvable Groups Are Not in FO+MOD+MÂJ2[REG]

Motivated by the open question whether

Regular Languages Definable by Majority Quantifiers with Two Variables

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Linear circuits, two-variable logic and weakly blocked monoids

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The lower reaches of circuit uniformity

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Practical Graph Isomorphism for Graphlet Data Mining in Protein Structures

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Low uniform versions of NC1.

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Regular Languages in MAJ[>] with three variables.

we consider the case of linear size TC0. We use the connections between circuits, logic, and algebra, in particular the characterization of

Typed Monoids - An Eilenberg-like Theorem for non regular Languages.

\mbox{TC{

An Approach to characterize the Regular Languages in TC0 with Linear Wires.

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