On Deterministic Finite Automata and Syntactic Monoid Size, Continued

  • Markus Holzer
  • Barbara König
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2710)


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 with n = k + 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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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Markus Holzer
    • 1
  • Barbara König
    • 1
  1. 1.Institut für InformatikTechnische Universität MünchenGarching bei MünchenGermany

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