Experiments with Synchronizing Automata

  • Andrzej Kisielewicz
  • Jakub Kowalski
  • Marek SzykułaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9705)


We have improved an algorithm generating synchronizing automata with a large length of the shortest reset words. This has been done by refining some known results concerning bounds on the reset length. Our improvements make possible to consider a number of conjectures and open questions concerning synchronizing automata, checking them for automata with a small number of states and discussing the results. In particular, we have verified the Černý conjecture for all binary automata with at most 12 states, and all ternary automata with at most 8 states.


Synchronous Automata Reset Word Binary Automata Worst-case Length Aperiodic Automata 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



We thank Mikhail Volkov for suggesting Conjecture 4, and Mikhail Berlinkov for observing that the bound for one-cluster automata can be improved for periodic subsets on the cycle, which leaded to an improvement of our algorithm. We thank also Vojtěch Vorel for discussing the problem of avoiding states and sharing the series. The main part of the computations was performed on a grid that belongs to Institute of Computer Science of Jagiellonian University (thanks to Adam Roman).


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Andrzej Kisielewicz
    • 1
  • Jakub Kowalski
    • 1
  • Marek Szykuła
    • 1
    Email author
  1. 1.Department of Mathematics and Computer ScienceUniversity of WrocławWrocławPoland

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