Publication Details

Solutions To Four Open Problems Concerning Controlled Pure Grammar Systems

MEDUNA, A.; VRÁBEL, L.; ZEMEK, P. Solutions To Four Open Problems Concerning Controlled Pure Grammar Systems. International Journal of Computer Mathematics, 2014, vol. 91, no. 6, p. 1156-1169. ISSN: 0020-7160.
Czech title
Řešení čtyř otevřených problémů týkajících se řízených čistých gramatických systémů
Type
journal article
Language
English
Authors
Meduna Alexandr, prof. RNDr., CSc. (DIFS)
Vrábel Lukáš, Ing.
Zemek Petr, Ing., Ph.D.
URL
Keywords

formal languages, pure grammar systems, controlled leftmost derivations, regular languages, erasing rules

Abstract

In this paper, we address several open problems concerning pure grammar systems (pGSs) and their controlled versions. More specifically, we prove the following four results. (I) Regular-controlled pGSs having a single component define the family of regular languages. (II) pGSs having two components controlled by infinite regular languages define the family of recursively enumerable languages. (III) Regular-controlled pGSs without any erasing rules define the family of regular languages not containing the empty string. (IV) pGSs define a proper subfamily of the family of regular languages.

Published
2014
Pages
1156–1169
Journal
International Journal of Computer Mathematics, vol. 91, no. 6, ISSN 0020-7160
DOI
10.1080/00207160.2013.829214
UT WoS
000340826000002
EID Scopus
2-s2.0-84906788547
BibTeX 
@article{BUT111482,
  author="Alexandr {Meduna} and Lukáš {Vrábel} and Petr {Zemek}",
  title="Solutions To Four Open Problems Concerning Controlled Pure Grammar Systems",
  journal="International Journal of Computer Mathematics",
  year="2014",
  volume="91",
  number="6",
  pages="1156--1169",
  doi="10.1080/00207160.2013.829214",
  issn="0020-7160",
  url="http://www.tandfonline.com/doi/abs/10.1080/00207160.2013.829214"
}
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