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Acta Informatica

, Volume 49, Issue 2, pp 55–68 | Cite as

Nonterminal complexity of one-sided random context grammars

  • Alexander Meduna
  • Petr Zemek
Original Article

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.

Keywords

Induction Hypothesis Induction Step Sentential Form Descriptional Complexity Formal Language Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Department of Information Systems, Faculty of Information Technology, IT4Innovations Centre of ExcellenceBrno University of TechnologyBrnoCzech Republic

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