Publication Details

Jumping Grammars

KŘIVKA Zbyněk and MEDUNA Alexander. Jumping Grammars. International Journal of Foundations of Computer Science, vol. 26, no. 6, pp. 709-731. ISSN 0129-0541.
Czech title
Skákající gramatiky
Type
journal article
Language
english
Authors
Keywords

Modified grammars; discontinuous rewriting; generative power; jumping finite automata; semilinearity; finite index.

Abstract

This paper introduces and studies jumping grammars, which represent a grammatical counterpart to the recently introduced jumping automata. These grammars are conceptualized just like classical grammars except that during the applications of their productions, they can jump over symbols in either direction within the rewritten strings. More precisely, a jumping grammar rewrites a string z according to a rule x -> y in such a way that it selects an occurrence of x in z, erases it, and inserts y anywhere in the rewritten string, so this insertion may occur at a different position than the erasure of x.

The paper concentrates its attention on investigating the generative power of jumping grammars. More specifically, it compares this power with that of jumping automata and that of classical grammars.  A special attention is paid to various context-free versions of jumping grammars, such as regular, right-linear, linear, and context-free grammars of finite index. In addition, we study the semilinearity of context-free, context-sensitive, and monotonous jumping grammars. We also demonstrate that the general versions of jumping grammars characterize the family of recursively enumerable languages. In its conclusion, the paper formulates several open problems and suggests future investigation areas.

Published
2015
Pages
709-731
Journal
International Journal of Foundations of Computer Science, vol. 26, no. 6, ISSN 0129-0541
DOI
UT WoS
000364655800004
EID Scopus
BibTeX
@ARTICLE{FITPUB10735,
   author = "Zbyn\v{e}k K\v{r}ivka and Alexander Meduna",
   title = "Jumping Grammars",
   pages = "709--731",
   journal = "International Journal of Foundations of Computer Science",
   volume = 26,
   number = 6,
   year = 2015,
   ISSN = "0129-0541",
   doi = "10.1142/S0129054115500409",
   language = "english",
   url = "https://www.fit.vut.cz/research/publication/10735"
}
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