Note on Reversal of Binary Regular Languages

  • Galina Jirásková
  • Juraj Šebej
Conference paper

DOI: 10.1007/978-3-642-22600-7_17

Part of the Lecture Notes in Computer Science book series (LNCS, volume 6808)
Cite this paper as:
Jirásková G., Šebej J. (2011) Note on Reversal of Binary Regular Languages. In: Holzer M., Kutrib M., Pighizzini G. (eds) Descriptional Complexity of Formal Systems. DCFS 2011. Lecture Notes in Computer Science, vol 6808. Springer, Berlin, Heidelberg

Abstract

We present binary deterministic finite automata of n states that meet the upper bound 2n on the state complexity of reversal. The automata have a single final state and are one-cycle-free-path, thus the witness languages are deterministic union-free. This result allows us to describe a binary language such that the nondeterministic state complexity of the language and of its complement is n and n + 1, respectively, while the state complexity of the language is 2n. We also show that there is no regular language with state complexity 2n such that both the language and its complement have nondeterministic state complexity n.

Keywords

Regular languages reversal state complexity nondeterministic state complexity deterministic union-free languages 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Galina Jirásková
    • 1
  • Juraj Šebej
    • 2
  1. 1.Mathematical InstituteSlovak Academy of SciencesKošiceSlovakia
  2. 2.Institute of Computer ScienceP.J. Šafárik UniversityKošiceSlovakia

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