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Nonterminal complexity of one-sided random context grammars

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Abstract

In the present paper, we study the nonterminal complexity of one-sided random context grammars. More specifically, we prove that every recursively enumerable language can be generated by a one-sided random context grammar with no more than ten nonterminals. An analogical result holds for thirteen nonterminals in terms of these grammars with the set of left random context rules coinciding with the set of right random context rules. Furthermore, we introduce the notion of a right random context nonterminal, defined as a nonterminal that appears on the left-hand side of a right random context rule. We demonstrate how to convert any one-sided random context grammar G to an equivalent one-sided random context grammar H with two right random context nonterminals. An analogical conversion is given in terms of (1) propagating one-sided random context grammars and (2) left random context nonterminals. In the conclusion, two open problems are stated.

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Authors and Affiliations

  1. Department of Information Systems, Faculty of Information Technology, IT4Innovations Centre of Excellence, Brno University of Technology, Božetěchova 1/2, 61266, Brno, Czech Republic

    Alexander Meduna & Petr Zemek

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  1. Alexander Meduna
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  2. Petr Zemek
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Correspondence to Alexander Meduna.

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Meduna, A., Zemek, P. Nonterminal complexity of one-sided random context grammars. Acta Informatica 49, 55–68 (2012). https://doi.org/10.1007/s00236-012-0150-6

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  • DOI: https://doi.org/10.1007/s00236-012-0150-6

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