Routes and Products of Monoids

Authors:
Alexandru Mateescu;Rudolf Freund
Affiliations:
Institut für Computersprachen Technische Universität Wien Favoritenstr. 9, A-1040 Wien, Austria. E-mail: rudi@emcc.at;Institut für Computersprachen Technische Universität Wien Favoritenstr. 9, A-1040 Wien, Austria. E-mail: rudi@emcc.at
Venue:
Fundamenta Informaticae - SPECIAL ISSUE ON TRAJECTORIES OF LANGUAGE THEORY Dedicated to the memory of Alexandru Mateescu
Year:
2006

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Abstract

We investigate the problem of finding monoids that recognize languages of the form L$_1$⋈$_T$L$_2$ where T is an arbitrary set of routes. We present a uniform method based on routes to find such monoids. Many classical operations from the theory of formal languages, such as catenation, bi-catenation, simple splicing, shuffle, literal shuffle, and insertion are shown to be just particular instances of the operation ⋈$_T$.