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The Hardest Language for Conjunctive Grammars

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Abstract

A famous theorem by Greibach (“The hardest context-free language”, SIAM J. Comp., 1973) states that there exists such a context-free language \(L_0\) that every context-free language over any alphabet is reducible to \(L_0\) by a homomorphic reduction—in other words, is representable as an inverse homomorphic image \(h^{-1}(L_0)\), for a suitable homomorphism h. This paper establishes similar characterizations for conjunctive grammars, that is, for grammars extended with a conjunction operator.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Turku, FI-20014, Turku, Finland

    Alexander Okhotin

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  1. Alexander Okhotin
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Correspondence to Alexander Okhotin .

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Editors and Affiliations

  1. Russian Academy of Sciences, St. Petersburg, Russia

    Alexander S. Kulikov

  2. Technische Universiteit Eindhoven, Eindhoven, The Netherlands

    Gerhard J. Woeginger

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Okhotin, A. (2016). The Hardest Language for Conjunctive Grammars. In: Kulikov, A., Woeginger, G. (eds) Computer Science – Theory and Applications. CSR 2016. Lecture Notes in Computer Science(), vol 9691. Springer, Cham. https://doi.org/10.1007/978-3-319-34171-2_24

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  • DOI: https://doi.org/10.1007/978-3-319-34171-2_24

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-34170-5

  • Online ISBN: 978-3-319-34171-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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