RAIRO - Theoretical Informatics and Applications

Research Article

On context-free rewriting with a simple restriction and its computational completeness

Tomáš Masopusta1 and Alexander Medunaa1

a1 Faculty of Information Technology, Brno University of Technology, Božetěchova 2, Brno 61266, Czech Republic. masopust@fit.vutbr.cz; meduna@fit.vutbr.cz


This paper discusses context-free rewriting systems in which there exist two disjoint finite sets of rules, and a symbol, referred to as a condition of applicability, is attached to each rule in either of these two sets. In one set, a rule with a symbol attached to it is applicable if the attached symbol occurs in the current rewritten string while in the other set, such a rule is applicable if the attached symbol does not occur there. The present paper demonstrates that these rewriting systems are computationally complete. From this main result, the paper derives several consequences and solves several open problems.

(Received May 29 2007)

(Accepted December 15 2008)

(Online publication March 6 2009)

Key Words:

  • Formal languages;
  • context-free grammar;
  • context-free rewriting system;
  • derivation restriction;
  • generative power.

Mathematics Subject Classification:

  • 68Q45;
  • 68Q42