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

  • Galina Jirásková
  • Tomáš Masopust
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7381)

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.

Keywords

State Complexity Regular Language Maximal State Reachable State Quadratic Time 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Galina Jirásková
    • 1
  • Tomáš Masopust
    • 2
  1. 1.Mathematical InstituteSlovak Academy of SciencesKošiceSlovak Republic
  2. 2.Institute of MathematicsAcademy of Sciences of the Czech RepublicBrnoCzech Republic

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