An Extremal Series of Eulerian Synchronizing Automata

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9840)


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.


Eulerian automaton Reset threshold Reset word Synchronizing automaton 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Institute of Computer ScienceUniversity of WrocławWrocławPoland
  2. 2.Faculty of Mathematics and PhysicsCharles UniversityPragueCzech Republic

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