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A Family of NFA’s Which Need 2n — α Deterministic States

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Mathematical Foundations of Computer Science 2000 (MFCS 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1893))

Abstract

We show that for all integers n ≥ 7 and α, such that 5 ≤ α ≤ 2n - 2 and satisfying some coprimality conditions, there exists a minimum n-state nondeterministic finite automaton that is equivalent to a minimum deterministic finite automaton with exactly 2n - α states.

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References

  1. M. Rabin and D. Scott, “Finite automata and their decision problems,” IBM J. Res. Develop. 3, pp. 114–125, 1959.

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  4. J. E. Hopcroft and J. D. Ullman, Introduction to automata theory, languages and computation, Addison-Wesley, 1979.

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  5. K. Iwama, Y. Kambayashi, and K. Takaki, “Tight bounds on the number of states of DFA’s that are equivalent to n-state NFA’s,” Theoretical Computer Science, to appear. (http://www.lab2.kuis.kyoto-u.ac.jp/iwama/NfaDfa.ps)

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Author information

Authors and Affiliations

  1. School of Informatics, Kyoto University, Japan

    Kazuo Iwama & Akihiro Matsuura

  2. Department of Computer Science, University of Warwick, UK

    Mike Paterson

Authors
  1. Kazuo Iwama
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  2. Akihiro Matsuura
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  3. Mike Paterson
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Aarhus, Ny Munkegade, Bldg. 540, 8000, Aarhus C, Denmark

    Mogens Nielsen

  2. Department of Computer Sciene, Comenius University, 84248, Bratislava, Slovakia

    Branislav Rovan

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© 2000 Springer-Verlag Berlin Heidelberg

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Iwama, K., Matsuura, A., Paterson, M. (2000). A Family of NFA’s Which Need 2n — α Deterministic States. In: Nielsen, M., Rovan, B. (eds) Mathematical Foundations of Computer Science 2000. MFCS 2000. Lecture Notes in Computer Science, vol 1893. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44612-5_39

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  • DOI: https://doi.org/10.1007/3-540-44612-5_39

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67901-1

  • Online ISBN: 978-3-540-44612-5

  • eBook Packages: Springer Book Archive

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