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One-Sided Random Context Grammars: A Survey

  • Alexander Meduna
  • Petr Zemek
Chapter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8808)

Abstract

Recall that the notion of a one-sided random context grammar is based upon a finite set of context-free rules, each of which may be extended by finitely many permitting and forbidding nonterminal symbols. The set of all these rules is divided into two sets—the set of left random context rules and the set of right random context rules. When applying a left random context rule, the grammar checks the existence and absence of its permitting and forbidding symbols, respectively, in the prefix to the left of the rewritten nonterminal. Analogically, when applying a right random context rule, it checks the existence and absence of its permitting and forbidding symbols, respectively, only in the suffix to the right of the rewritten nonterminal.

This paper gives a survey of the established results concerning one-sided random context grammars. These results concern their generative power, normal forms, size reduction, and conceptual modifications, which represent both restricted and generalized versions of their standard concepts. Perhaps most importantly and surprisingly, the paper points out that propagating versions of one-sided random context grammars characterize the family of context-sensitive languages, and with erasing rules, they characterize the family of recursively enumerable languages; as a result, they are stronger than ordinary random context grammars. Many open problem areas are suggested.

Keywords

Formal language theory Regulated rewriting Random context grammars One-sided random context grammars Generative power Normal forms Reduction Leftmost derivations Generalized versions Survey 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

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

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