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International Conference on Developments in Language Theory

DLT 2014: Developments in Language Theory pp 49–60Cite as

Semisimple Synchronizing Automata and the Wedderburn-Artin Theory

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8633))

Abstract

We approach Černý’s conjecture using the Wedderburn- Artin theory. We first introduce the radical ideal of a synchronizing automaton, and then the natural notion of semisimple synchronizing automata. This is a rather broad class since it contains simple synchronizing automata like those in Černý’s series. Furthermore, semisimplicity gives the advantage of “factorizing” the problem of finding a synchronizing word into the sub-problems of finding words that are zeros in the projections into the simple components in the Wedderburn-Artin decomposition. This situation is applied to prove that Černý’s conjecture holds for the class of strongly semisimple synchronizing automata. These are automata whose sets of synchronizing words are cyclic ideals, or equivalently are ideal regular languages which are closed by takings roots.

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Author information

Authors and Affiliations

  1. Centro de Matemática, Faculdade de Ciências, Universidade do Porto, 4169-007, Porto, Portugal

    Jorge Almeida & Emanuele Rodaro

Authors
  1. Jorge Almeida
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  2. Emanuele Rodaro
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Editor information

Editors and Affiliations

  1. Institute of Mathematics and Computer Science, Ural Federal University, pr. Lenina, 51, 620000, Ekaterinburg, Russia

    Arseny M. Shur  & Mikhail V. Volkov  & 

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Almeida, J., Rodaro, E. (2014). Semisimple Synchronizing Automata and the Wedderburn-Artin Theory. In: Shur, A.M., Volkov, M.V. (eds) Developments in Language Theory. DLT 2014. Lecture Notes in Computer Science, vol 8633. Springer, Cham. https://doi.org/10.1007/978-3-319-09698-8_5

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  • DOI: https://doi.org/10.1007/978-3-319-09698-8_5

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-09697-1

  • Online ISBN: 978-3-319-09698-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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