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On the Transformation of LL(k)-linear to LL(1)-linear Grammars

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A Correction to this article was published on 11 February 2023

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Abstract

It is proved that every LL(k)-linear grammar can be transformed to an equivalent LL(1)-linear grammar. The transformation incurs a blow-up in the number of nonterminal symbols by a factor of m2k−O(1), where m is the size of the alphabet. A close lower bound is established: for certain LL(k)-linear grammars with n nonterminal symbols, every equivalent LL(1)-linear grammar must have at least \(n \cdot (m-1)^{2k-O(\log k)}\) nonterminal symbols.

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Acknowledgements

The authors are grateful to Henning Fernau and Dominik Kempa for interesting comments on the conference paper, and, in particular, for suggesting the idea of Section 7. Thanks are due to an anonymous referee for careful reading, and for convincing the authors to make numerous improvements to the presentation.

This work was carried out during the first author’s appointment at the Leonhard Euler International Mathematical Institute at St. Petersburg State University, Russia, and was supported by the Ministry of Science and Higher Education of the Russian Federation, agreement 075-15-2022-287.

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Authors and Affiliations

  1. Helmholtz Institute for Pharmaceutical Research Saarland (HIPS), Helmholtz Centre for Infection Research, Campus E8.1, 66123, Saarbrücken, Germany

    Ilya Olkhovsky

  2. Department of Mathematics and Computer Science, St. Petersburg State University, 14th Line V. O., 29, Saint Petersburg, 199178, Russia

    Ilya Olkhovsky & Alexander Okhotin

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  1. Ilya Olkhovsky
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  2. Alexander Okhotin
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Correspondence to Ilya Olkhovsky.

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A preliminary version of this paper was presented at Computer Science in Russia (CSR 2020) conference, and its extended abstract appeared in the proceedings.

The original online version of this article was revised to update the affiliation of corresponding author Ilya Olkhovsky.

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Olkhovsky, I., Okhotin, A. On the Transformation of LL(k)-linear to LL(1)-linear Grammars. Theory Comput Syst 67, 234–262 (2023). https://doi.org/10.1007/s00224-022-10108-6

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