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Unambiguous Finite Automata over a Unary Alphabet

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Mathematical Foundations of Computer Science 2010 (MFCS 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6281))

Abstract

Nondeterministic finite automata (NFA) with at most one accepting computation on every input string are known as unambiguous finite automata (UFA). This paper considers UFAs over a unary alphabet, and determines the exact number of states in DFAs needed to represent unary languages recognized by n-state UFAs: the growth rate of this function is \(e^{\Theta(\sqrt[3]{n \ln^2 n})}\). The conversion of an n-state unary NFA to a UFA requires UFAs with \(g(n)+O(n^2)=e^{\sqrt{n \ln n}(1+o(1))}\) states, where g(n) is Landau’s function. In addition, it is shown that the complement of n-state unary UFAs requires up to at least n 2 − o(1) states in an NFA, while the Kleene star requires up to exactly (n − 1)2 + 1 states.

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Authors and Affiliations

  1. Department of Mathematics, University of Turku, Academy of Finland, Turku, FI–20014, Finland

    Alexander Okhotin

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  1. Alexander Okhotin
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Editors and Affiliations

  1. Falculty of Informatics, Masaryk University, Botanicka 68a, 602 00, Brno, Czech Republic

    Petr Hliněný

  2. Faculty of Informatics, Masaryk University, Botanicka 68a, 602 00, Brno, Czech Republic

    Antonín Kučera

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Okhotin, A. (2010). Unambiguous Finite Automata over a Unary Alphabet. In: Hliněný, P., Kučera, A. (eds) Mathematical Foundations of Computer Science 2010. MFCS 2010. Lecture Notes in Computer Science, vol 6281. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15155-2_49

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  • DOI: https://doi.org/10.1007/978-3-642-15155-2_49

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15154-5

  • Online ISBN: 978-3-642-15155-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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