On context-free rewriting with a simple restriction and its computational completeness
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 43 (2009) no. 2, pp. 365-378.

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.

DOI: 10.1051/ita/2009002
Classification: 68Q45,  68Q42
Keywords: formal languages, context-free grammar, context-free rewriting system, derivation restriction, generative power
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Masopust, Tomáš; Meduna, Alexander. On context-free rewriting with a simple restriction and its computational completeness. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 43 (2009) no. 2, pp. 365-378. doi : 10.1051/ita/2009002. http://www.numdam.org/articles/10.1051/ita/2009002/

[1] J. Dassow and G. Păun, Regulated Rewriting in Formal Language Theory. Springer-Verlag, Berlin (1989). | MR | Zbl

[2] O. Mayer, Some restrictive devices for context-free grammars. Inform. Control 20 (1972) 69-92. | MR | Zbl

[3] A. Meduna and A. Gopalaratnam, On semi-conditional grammars with productions having either forbidding or permitting conditions. Acta Cybernetica 11 (1994) 307-324. | MR | Zbl

[4] A. Meduna and M. Švec, Grammars with Context Conditions and Their Applications. John Wiley & Sons, New York (2005). | MR | Zbl

[5] G. Păun, A variant of random context grammars: Semi-conditional grammars. Theoret. Comput. Sci. 41 (1985) 1-17. | MR | Zbl

[6] A. Salomaa, Formal languages. Academic Press, New York (1973). | MR | Zbl

[7] A.P.J. Van Der Walt, Random context grammars, in Proceedings of the Symposium on Formal Languages (1970).

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