A Fast Algorithm Finding the Shortest Reset Words

  • Andrzej Kisielewicz
  • Jakub Kowalski
  • Marek Szykuła
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7936)

Abstract

In this paper we present a new fast algorithm for finding minimal reset words for finite synchronizing automata, which is a problem appearing in many practical applications. The problem is known to be computationally hard, so our algorithm is exponential in the worst case, but it is faster than the algorithms used so far and it performs well on average. The main idea is to use a bidirectional BFS and radix (Patricia) tries to store and compare subsets. Also a number of heuristics are applied. We give both theoretical and practical arguments showing that the effective branching factor is considerably reduced. As a practical test we perform an experimental study of the length of the shortest reset word for random automata with n ≤ 300 states and 2 input letters. In particular, we obtain a new estimation of the expected length of the shortest reset word \(\approx 2.5\sqrt{n-5}\).

Keywords

Synchronizing automaton synchronizing word Černý conjecture 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Andrzej Kisielewicz
    • 1
    • 2
  • Jakub Kowalski
    • 1
  • Marek Szykuła
    • 1
  1. 1.Department of Mathematics and Computer ScienceUniversity of WrocławPoland
  2. 2.Institute of Mathematics and Computer ScienceUniversity of OpolePoland

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