A Pumping Lemma for Permitting Semi-Conditional Languages

Zsolt Gazdag, Krisztián Tichler, E. Csuhaj-Varjú

Research output: Contribution to journalArticle

Abstract

Permitting semi-conditional grammars (pSCGs) are extensions of context-free grammars where each rule is associated with a word w and such a rule can be applied to a sentential form u only if w is a subword of u. We consider permitting generalized SCGs (pgSCGs) where each rule r is associated with a set of words P and r is applicable only if every word in P occurs in u. We investigate the generative power of pgSCGs with no erasing rules and prove a pumping lemma for their languages. Using this lemma we show that pgSCGs are strictly weaker than context-sensitive grammars. This solves a long-lasting open problem concerning the generative power of pSCGs. Moreover, we give a comparison of the generating power of pgSCGs and that of forbidding random context grammars with no erasing rules.

Original languageEnglish
Pages (from-to)73-92
Number of pages20
JournalInternational Journal of Foundations of Computer Science
Volume30
Issue number1
DOIs
Publication statusPublished - Jan 1 2019

Fingerprint

Context sensitive grammars
Context free grammars

Keywords

  • generative power
  • permitting context
  • Semi-conditional grammars

ASJC Scopus subject areas

  • Computer Science (miscellaneous)

Cite this

A Pumping Lemma for Permitting Semi-Conditional Languages. / Gazdag, Zsolt; Tichler, Krisztián; Csuhaj-Varjú, E.

In: International Journal of Foundations of Computer Science, Vol. 30, No. 1, 01.01.2019, p. 73-92.

Research output: Contribution to journalArticle

@article{3dc179e40f1a409ca63c4c5233653837,
title = "A Pumping Lemma for Permitting Semi-Conditional Languages",
abstract = "Permitting semi-conditional grammars (pSCGs) are extensions of context-free grammars where each rule is associated with a word w and such a rule can be applied to a sentential form u only if w is a subword of u. We consider permitting generalized SCGs (pgSCGs) where each rule r is associated with a set of words P and r is applicable only if every word in P occurs in u. We investigate the generative power of pgSCGs with no erasing rules and prove a pumping lemma for their languages. Using this lemma we show that pgSCGs are strictly weaker than context-sensitive grammars. This solves a long-lasting open problem concerning the generative power of pSCGs. Moreover, we give a comparison of the generating power of pgSCGs and that of forbidding random context grammars with no erasing rules.",
keywords = "generative power, permitting context, Semi-conditional grammars",
author = "Zsolt Gazdag and Kriszti{\'a}n Tichler and E. Csuhaj-Varj{\'u}",
year = "2019",
month = "1",
day = "1",
doi = "10.1142/S0129054119400045",
language = "English",
volume = "30",
pages = "73--92",
journal = "International Journal of Foundations of Computer Science",
issn = "0129-0541",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "1",

}

TY - JOUR

T1 - A Pumping Lemma for Permitting Semi-Conditional Languages

AU - Gazdag, Zsolt

AU - Tichler, Krisztián

AU - Csuhaj-Varjú, E.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - Permitting semi-conditional grammars (pSCGs) are extensions of context-free grammars where each rule is associated with a word w and such a rule can be applied to a sentential form u only if w is a subword of u. We consider permitting generalized SCGs (pgSCGs) where each rule r is associated with a set of words P and r is applicable only if every word in P occurs in u. We investigate the generative power of pgSCGs with no erasing rules and prove a pumping lemma for their languages. Using this lemma we show that pgSCGs are strictly weaker than context-sensitive grammars. This solves a long-lasting open problem concerning the generative power of pSCGs. Moreover, we give a comparison of the generating power of pgSCGs and that of forbidding random context grammars with no erasing rules.

AB - Permitting semi-conditional grammars (pSCGs) are extensions of context-free grammars where each rule is associated with a word w and such a rule can be applied to a sentential form u only if w is a subword of u. We consider permitting generalized SCGs (pgSCGs) where each rule r is associated with a set of words P and r is applicable only if every word in P occurs in u. We investigate the generative power of pgSCGs with no erasing rules and prove a pumping lemma for their languages. Using this lemma we show that pgSCGs are strictly weaker than context-sensitive grammars. This solves a long-lasting open problem concerning the generative power of pSCGs. Moreover, we give a comparison of the generating power of pgSCGs and that of forbidding random context grammars with no erasing rules.

KW - generative power

KW - permitting context

KW - Semi-conditional grammars

UR - http://www.scopus.com/inward/record.url?scp=85062560327&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85062560327&partnerID=8YFLogxK

U2 - 10.1142/S0129054119400045

DO - 10.1142/S0129054119400045

M3 - Article

AN - SCOPUS:85062560327

VL - 30

SP - 73

EP - 92

JO - International Journal of Foundations of Computer Science

JF - International Journal of Foundations of Computer Science

SN - 0129-0541

IS - 1

ER -