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On Deterministic Finite Automata and Syntactic Monoid Size, Continued

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Developments in Language Theory (DLT 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2710))

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Abstract

We continue our investigation on the relationship between regular languages and syntactic monoid size. In this paper we confirm the conjecture on two generator transformation semigroups. We show that for every prime n ≥ 7 there exist natural numbers k and ℓ with n = k + ℓ such that the semigroup U k,ℓ is maximal w.r.t. its size among all (transformation) semigroups which can be generated with two generators. This significantly tightens the bound on the syntactic monoid size of languages accepted by n-state deterministic finite automata with binary input alphabet. As a by-product of our investigations we are able to determine the maximal size among all semigroups generated by two transformations, where one is a permutation with a single cycle and the other is a non-bijective mapping.

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Author information

Authors and Affiliations

  1. Institut für Informatik, Technische Universität München, Boltzmannstraße 3, D-85748, Garching bei München, Germany

    Markus Holzer & Barbara König

Authors
  1. Markus Holzer
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  2. Barbara König
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Editor information

Editors and Affiliations

  1. Department of Informatics, University of Szeged, Árpád tér 2, 6720, Szeged, Hungary

    Zoltán Ésik  & Zoltán Fülöp  & 

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Holzer, M., König, B. (2003). On Deterministic Finite Automata and Syntactic Monoid Size, Continued. In: Ésik, Z., Fülöp, Z. (eds) Developments in Language Theory. DLT 2003. Lecture Notes in Computer Science, vol 2710. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45007-6_28

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  • DOI: https://doi.org/10.1007/3-540-45007-6_28

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40434-7

  • Online ISBN: 978-3-540-45007-8

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