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A new approach to formal language theory by kolmogorov complexity

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Automata, Languages and Programming (ICALP 1989)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 372))

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Abstract

We introduce Kolmogorov complexity as a new technique in Formal Language Theory. We give an alternative for pumping lemma(s) and a new characterization for regular languages. For the separation of deterministic contextfree languages and contextfree languages no pumping lemmas or any other general method was known. We give a first general technique to separate these classes, and illustrate its use on four examples previously requiring labourous ad hoc methods. The approach is also successful at the high end of the Chomsky hierarchy since one can quantify nonrecursiveness in terms of Kolmogorov complexity. We also give a new proof, using Kolmogorov complexity, of Yao and Rivest's result that k + 1 heads are better than k heads.

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Author information

Authors and Affiliations

  1. Department of Computer Science, York University, M3J 1P3, North York, Ontario, Canada

    Ming Li

  2. Centrum voor Wiskunde en Informatica, Kruislaan 413, 1098 SJ, Amsterdam, The Netherlands

    Paul M. B. Vitanyi

  3. Faculteit Wiskunde en Informatica, Universiteit van Amsterdam, The Netherlands

    Paul M. B. Vitanyi

Authors
  1. Ming Li
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  2. Paul M. B. Vitanyi
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Giorgio Ausiello Mariangiola Dezani-Ciancaglini Simonetta Ronchi Della Rocca

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© 1989 Springer-Verlag Berlin Heidelberg

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Li, M., Vitanyi, P.M.B. (1989). A new approach to formal language theory by kolmogorov complexity. In: Ausiello, G., Dezani-Ciancaglini, M., Della Rocca, S.R. (eds) Automata, Languages and Programming. ICALP 1989. Lecture Notes in Computer Science, vol 372. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0035780

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  • DOI: https://doi.org/10.1007/BFb0035780

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  • Print ISBN: 978-3-540-51371-1

  • Online ISBN: 978-3-540-46201-9

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