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Approximating the Minimum Length of Synchronizing Words Is Hard

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Abstract

We prove that, unless P=NP, no polynomial-time algorithm can approximate the minimum length of reset words for a given synchronizing automaton within a constant factor.

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Notes

  1. This result appeared also in [18]; however, a false reduction was used there.

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Acknowledgements

The author acknowledges support from the Russian Foundation for Basic Research, grant 13-01-00852, and by the Presidential Program for young researchers, grant MK-266.2012.1. The author is also thankful to the anonymous referees for several useful remarks.

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  1. Institute of Mathematics and Computer Science, Ural Federal University, 620000, Ekaterinburg, Russia

    Mikhail V. Berlinkov

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  1. Mikhail V. Berlinkov
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Correspondence to Mikhail V. Berlinkov.

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Berlinkov, M.V. Approximating the Minimum Length of Synchronizing Words Is Hard. Theory Comput Syst 54, 211–223 (2014). https://doi.org/10.1007/s00224-013-9511-y

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