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The Hardest LL(k) Language

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Developments in Language Theory (DLT 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12811))

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Abstract

This paper establishes an analogue of Greibach’s hardest language theorem (“The hardest context-free language”, SIAM J. Comp., 1973) for the subfamily of LL languages. The first result is that there is a language \(L_0\) defined by an LL(1) grammar in the Greibach normal form, to which every language L defined by an LL(1) grammar in the Greibach normal form can be reduced by a homomorphism, that is, \(w \in L\) if and only if \(h(w) \in L_0\). Then it is shown that this statement does not hold for LL(k) languages. The second hardest language theorem is then established in the following form: there is a language \(L_0\) defined by an LL(1) grammar in the Greibach normal form, such that, for every language L defined by an LL(k) grammar, there exists a homomorphism h, for which \(w \in L\) if and only if \(h(w \$) \in L_0\), where \(\$\) is a new symbol.

This work was supported by the Russian Science Foundation, project 18-11-00100.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, St. Petersburg State University, 7/9 Universitetskaya nab., Saint Petersburg, 199034, Russia

    Mikhail Mrykhin & Alexander Okhotin

Authors
  1. Mikhail Mrykhin
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  2. Alexander Okhotin
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Editors and Affiliations

  1. University of Porto, Porto, Portugal

    Nelma Moreira

  2. University of Porto, Porto, Portugal

    Rogério Reis

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Mrykhin, M., Okhotin, A. (2021). The Hardest LL(k) Language. In: Moreira, N., Reis, R. (eds) Developments in Language Theory. DLT 2021. Lecture Notes in Computer Science(), vol 12811. Springer, Cham. https://doi.org/10.1007/978-3-030-81508-0_25

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  • DOI: https://doi.org/10.1007/978-3-030-81508-0_25

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-81507-3

  • Online ISBN: 978-3-030-81508-0

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