, Volume 63, Issue 3, pp 571–587 | Cite as

Pairs of Complementary Unary Languages with “Balanced” Nondeterministic Automata



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 still require a superpolynomial number of states, at least \(e^{\Omega(\sqrt[3]{n\cdot\ln^{2}n})}\). Actually, L and Lc are “balanced” not only in the number of states but, moreover, they 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 Unary automata 


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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Computer ScienceP. J. Šafárik UniversityKošiceSlovakia
  2. 2.Dipartimento di Informatica e ComunicazioneUniversità degli Studi di MilanoMilanItaly

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