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On the State and Computational Complexity of the Reverse of Acyclic Minimal DFAs

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Implementation and Application of Automata (CIAA 2012)

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

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Abstract

We study the state complexity of the reverse of acyclic minimal deterministic finite automata, and the computational complexity of the following problem: Given an acyclic minimal DFA, is the minimal DFA for the reverse also acyclic? Note that we allow self-loops in acyclic automata. We show that there exists a language accepted by an acyclic minimal DFA such that the minimal DFA for its reverse is exponential with respect to the number of states, and we establish a tight bound on the state complexity of the reverse of acyclic DFAs. We also give a direct proof of the fact that the minimal DFA for the reverse is acyclic if and only if the original acyclic minimal DFA satisfies a certain structural property, which can be tested in quadratic time.

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Author information

Authors and Affiliations

  1. Mathematical Institute, Slovak Academy of Sciences, Grešákova 6, 040 01, Košice, Slovak Republic

    Galina Jirásková

  2. Institute of Mathematics, Academy of Sciences of the Czech Republic, Žižkova 22, 616 62, Brno, Czech Republic

    Tomáš Masopust

Authors
  1. Galina Jirásková
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  2. Tomáš Masopust
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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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Jirásková, G., Masopust, T. (2012). On the State and Computational Complexity of the Reverse of Acyclic Minimal DFAs. 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_20

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  • DOI: https://doi.org/10.1007/978-3-642-31606-7_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31605-0

  • Online ISBN: 978-3-642-31606-7

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