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Recognisable Languages over Monads

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Developments in Language Theory (DLT 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9168))

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Abstract

This paper proposes monads as a framework for algebraic language theory. Examples of monads include words and trees, finite and infinite. Each monad comes with a standard notion of an algebra, called an Eilenberg-Moore algebra, which generalises algebras studied in language theory like semigroups or \(\omega \)-semigroups. On the abstract level of monads one can prove theorems like the Myhill-Nerode theorem, the Eilenberg theorem; one can also define profinite objects.

M. Bojańczyk—Author supported by the Polish NCN grant 2014-13/B/ST6/03595.

A full version of this paper is available at http://arxiv.org/abs/1502.04898. The full version includes many examples of monads, proofs, stronger versions of theorems from this extended abstract, and entirely new theorems.

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Authors and Affiliations

  1. University of Warsaw, Warsaw, Poland

    Mikołaj Bojańczyk

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  1. Mikołaj Bojańczyk
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Correspondence to Mikołaj Bojańczyk .

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Editors and Affiliations

  1. University of Liverpool, Liverpool, United Kingdom

    Igor Potapov

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Bojańczyk, M. (2015). Recognisable Languages over Monads. In: Potapov, I. (eds) Developments in Language Theory. DLT 2015. Lecture Notes in Computer Science(), vol 9168. Springer, Cham. https://doi.org/10.1007/978-3-319-21500-6_1

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  • DOI: https://doi.org/10.1007/978-3-319-21500-6_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-21499-3

  • Online ISBN: 978-3-319-21500-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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