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Matrix Mortality and the Černý-Pin Conjecture

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Developments in Language Theory (DLT 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5583))

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Abstract

In this paper, we establish the Černý-Pin conjecture for automata with the property that their transition monoid cannot recognize the language {a,b}* ab{a,b}*. For the subclass of automata whose transition monoids have the property that each regular -class is a subsemigroup, we give a tight bound on lengths of reset words for synchronizing automata thereby answering a question of Volkov.

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Authors and Affiliations

  1. Departamento de Matemática Pura, Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre, 687, 4169-007, Porto, Portugal

    Jorge Almeida

  2. School of Mathematics and Statistics, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario, K1S 5B6, Canada

    Benjamin Steinberg

Authors
  1. Jorge Almeida
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  2. Benjamin Steinberg
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Editors and Affiliations

  1. Institut für Formale Methoden der Informatik, FMI, Universität Stuttgart, Universitätsstrasse 38, 70569, Stuttgart, Germany

    Volker Diekert  & Dirk Nowotka  & 

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Almeida, J., Steinberg, B. (2009). Matrix Mortality and the Černý-Pin Conjecture. In: Diekert, V., Nowotka, D. (eds) Developments in Language Theory. DLT 2009. Lecture Notes in Computer Science, vol 5583. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02737-6_5

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  • DOI: https://doi.org/10.1007/978-3-642-02737-6_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02736-9

  • Online ISBN: 978-3-642-02737-6

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