Publication Details

Nonterminal Complexity of One-Sided Random Context Grammars

MEDUNA, A.; ZEMEK, P. Nonterminal Complexity of One-Sided Random Context Grammars. Acta Informatica, 2012, vol. 49, no. 2, p. 55-68. ISSN: 0001-5903.
Czech title
Neterminální složitost jednostranných gramatik s nahodilým kontextem
Type
journal article
Language
English
Authors
Meduna Alexandr, prof. RNDr., CSc. (DIFS)
Zemek Petr, Ing., Ph.D.
URL
Keywords

Formal languages, nonterminal complexity, one-sided random context grammars,
random context nonterminals

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.

Published
2012
Pages
55–68
Journal
Acta Informatica, vol. 49, no. 2, ISSN 0001-5903
DOI
10.1007/s00236-012-0150-6
UT WoS
000301374500001
BibTeX 
@article{BUT91445,
  author="Alexandr {Meduna} and Petr {Zemek}",
  title="Nonterminal Complexity of One-Sided Random Context Grammars",
  journal="Acta Informatica",
  year="2012",
  volume="49",
  number="2",
  pages="55--68",
  doi="10.1007/s00236-012-0150-6",
  issn="0001-5903",
  url="http://www.springerlink.com/content/5822041380786746/"
}
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