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International Conference on Implementation and Application of Automata

CIAA 2012: Implementation and Application of Automata pp 171–179Cite as

Synchronizing Automata of Bounded Rank

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7381))

Abstract

We reduce the problem of synchronization of an n-state automaton with letters of rank at most r < n to the problem of synchronization of an r-state automaton with constraints given by a regular language. Using this technique we construct a series of synchronizing n-state automata in which every letter has rank r < n and whose reset threshold is at least r 2 − r − 1 Moreover, if \(r > \frac{n}{2}\), such automata are strongly connected.

Supported by the Russian Foundation for Basic Research, grant 10-01-00793, and by the Presidential Program for young researchers, grant MK-266.2012.1. Author is also grateful to Erasmus Mundus Action 2 Partnerships — Triple I.

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Author information

Authors and Affiliations

  1. Institute of Mathematics and Computer Science, Ural Federal University, 620083, Ekaterinburg, Russia

    Vladimir V. Gusev

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  1. Vladimir V. Gusev
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Editors and Affiliations

  1. Departamento de Ciência de Computadores, Universidade do Porto, Faculdade de Ciências, Rua do Campo Alegre 1021-1055, 4169-007, Porto, Portugal

    Nelma Moreira  & Rogério Reis  & 

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Gusev, V.V. (2012). Synchronizing Automata of Bounded Rank. In: Moreira, N., Reis, R. (eds) Implementation and Application of Automata. CIAA 2012. Lecture Notes in Computer Science, vol 7381. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31606-7_15

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  • DOI: https://doi.org/10.1007/978-3-642-31606-7_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31605-0

  • Online ISBN: 978-3-642-31606-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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