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An Extremal Series of Eulerian Synchronizing Automata

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Developments in Language Theory (DLT 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9840))

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Abstract

We present an infinite series of n-state Eulerian automata whose reset words have length at least \((n^2-3)/2\). This improves the current lower bound on the length of shortest reset words in Eulerian automata. We conjecture that \((n^2-3)/2\) also forms an upper bound for this class and we experimentally verify it for small automata by an exhaustive computation.

M. Szykuła—Supported in part by the National Science Centre, Poland under project number 2015/17/B/ST6/01893.

V. Vorel—Research supported by the Czech Science Foundation grant GA14-10799S and the GAUK grant No. 52215.

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Authors and Affiliations

  1. Institute of Computer Science, University of Wrocław, Joliot-Curie 15, Wrocław, Poland

    Marek Szykuła

  2. Faculty of Mathematics and Physics, Charles University, Malostranské nám. 25, Prague, Czech Republic

    Vojtěch Vorel

Authors
  1. Marek Szykuła
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  2. Vojtěch Vorel
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Corresponding authors

Correspondence to Marek Szykuła or Vojtěch Vorel .

Editor information

Editors and Affiliations

  1. Université du Québec à Montréal , Montreal, Québec, Canada

    Srečko Brlek

  2. Dept Mathematiques, Univ du Quebec Montreal Dept Mathematiques, Montreal, Québec, Canada

    Christophe Reutenauer

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Szykuła, M., Vorel, V. (2016). An Extremal Series of Eulerian Synchronizing Automata. In: Brlek, S., Reutenauer, C. (eds) Developments in Language Theory. DLT 2016. Lecture Notes in Computer Science(), vol 9840. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53132-7_31

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  • DOI: https://doi.org/10.1007/978-3-662-53132-7_31

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  • Online ISBN: 978-3-662-53132-7

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