Minimal Reversible Deterministic Finite Automata

  • Markus Holzer
  • Sebastian Jakobi
  • Martin KutribEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9168)


We study reversible deterministic finite automata (REV-DFAs), that are partial deterministic finite automata whose transition function induces an injective mapping on the state set for every letter of the input alphabet. We give a structural characterization of regular languages that can be accepted by REV-DFAs. This characterization is based on the absence of a forbidden pattern in the (minimal) deterministic state graph. Again with a forbidden pattern approach, we also show that the minimality of REV-DFAs among all equivalent REV-DFAs can be decided. Both forbidden pattern characterizations give rise to NL-complete decision algorithms. In fact, our techniques allow us to construct the minimal REV-DFA for a given minimal DFA. These considerations lead to asymptotic upper and lower bounds on the conversion from DFAs to REV-DFAs. Thus, almost all problems that concern uniqueness and the size of minimal REV-DFAs are solved.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Markus Holzer
    • 1
  • Sebastian Jakobi
    • 1
  • Martin Kutrib
    • 1
    Email author
  1. 1.Institut für InformatikUniversität GiessenGiessenGermany

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