Pairs of Complementary Unary Languages with “Balanced” Nondeterministic Automata

  • Viliam Geffert
  • Giovanni Pighizzini
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6034)


For each sufficiently large N, there exists a unary regular language L such that both L and its complement Lc are accepted by unambiguous nondeterministic automata with at most N states while the smallest deterministic automata for these two languages require a superpolynomial number of states, at least \(e^{\Omega(\sqrt[3]{N\cdot\ln^{2}\!N})}\!\) . Actually, L and Lc are accepted by nondeterministic machines sharing the same transition graph, differing only in the distribution of their final states. As a consequence, the gap between the sizes of unary unambiguous self-verifying automata and deterministic automata is also superpolynomial.


finite state automata state complexity unary regular languages 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Viliam Geffert
    • 1
  • Giovanni Pighizzini
    • 2
  1. 1.Department of Computer ScienceP. J. Šafárik UniversityKošiceSlovakia
  2. 2.Dipartimento di Informatica e ComunicazioneUniversità degli Studi di MilanoMilanoItaly

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