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Varieties of languages

Branco, Mário J. J.

Proceedings of the Thematic Term on Semigroups, Algorithms, Automata and Languages (Coimbra, Portugal, 2001), G.M.S. Gomes et al. (Eds), World Scientific, Singapore, (2002), 91-132

In this article we give an overview of the algebraic theory of recognizable languages, namely Eilenberg's variety theory and its analogue for ordered monoids due to Pin. It also includes the descriptions of varieties of finite (ordered) monoids in terms of identities and some results on the power operator and Schutzenberger and Malcev products, including their interpretation in terms of languages.