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International Conference on Developments in Language Theory

DLT 2002: Developments in Language Theory pp 258–269Cite as

On Deterministic Finite Automata and Syntactic Monoid Size

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2450))

Abstract

We investigate the relationship between regular languages and syntactic monoid size. In particular, we consider the transformation monoids of n-state (minimal) deterministic finite automata. We show tight upper bounds on the syntactic monoid size, proving that an n- state deterministic finite automaton with singleton input alphabet (input alphabet with at least three letters, respectively) induces a linear (n n, respectively) size syntactic monoid. In the case of two letter input alphabet, we can show a lower bound of n n-( nℓ )ℓ!n k - ( nℓ )k kℓℓ for some natural numbers k and ℓ close to n/2, for the size of the syntactic monoid of a language accepted by an n-state deterministic finite automaton. This induces a family of deterministic finite automata such that the fraction of the size of the induced syntactic monoid and n n tends to 1 as n goes to infinity.

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Author information

Authors and Affiliations

  1. Institut für Informatik, Technische Universität München, Arcisstraβe 21, D-80290, 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. Faculty of Science and Faculty of Engineering, Kyoto Sangyo University, 603-8555, Kyoto, Japan

    Masami Ito  & Masafumi Toyama  & 

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Holzer, M., König, B. (2003). On Deterministic Finite Automata and Syntactic Monoid Size. In: Ito, M., Toyama, M. (eds) Developments in Language Theory. DLT 2002. Lecture Notes in Computer Science, vol 2450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45005-X_22

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  • DOI: https://doi.org/10.1007/3-540-45005-X_22

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40431-6

  • Online ISBN: 978-3-540-45005-4

  • eBook Packages: Springer Book Archive

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