Synchronization Problems in Automata Without Non-trivial Cycles

  • Andrew RyzhikovEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10329)


We study the computational complexity of various problems related to synchronization of weakly acyclic automata, a subclass of widely studied aperiodic automata. We provide upper and lower bounds on the length of a shortest word synchronizing a weakly acyclic automaton or, more generally, a subset of its states, and show that the problem of approximating this length is hard. We also show inapproximability of the problem of computing the rank of a subset of states in a binary weakly acyclic automaton and prove that several problems related to recognizing a synchronizing subset of states in such automata are NP-complete.


Synchronizing automata Computational complexity Weakly acyclic automata Subset rank 



We would like to thank Vladimir Gusev and Ilia Fridman for very useful discussions, and Mikhail V. Volkov and anonymous reviewers for their great contribution to the improvement of the paper.


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Laboratoire G-SCOPUniversité Grenoble AlpesGrenobleFrance
  2. 2.United Institute of Informatics Problems of NASBMinskBelarus

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