On Müller context-free grammars

Z. Ésik, Szabolcs Iván

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We define context-free grammars with Müller acceptance condition that generate languages of countable words. We establish several elementary properties of the class of Müller context-free languages including closure properties and others. We show that every Müller context-free grammar can be transformed into a normal form grammar in polynomial space, and then we show that many decision problems can be decided in polynomial time for Müller context-free grammars in normal form. These decision problems include deciding whether the language generated by a normal form grammar contains only well-ordered, scattered, or dense words. In a further result, we establish a limitedness property of Müller context-free grammars: if the language generated by a grammar contains only scattered words, then either there is an integer n such that each word of the language has Hausdorff rank at most n, or the language contains scattered words of arbitrarily large Hausdorff rank. We also show that it is decidable which of the two cases applies.

Original languageEnglish
Pages (from-to)17-32
Number of pages16
JournalTheoretical Computer Science
Volume416
DOIs
Publication statusPublished - Jan 27 2012

Fingerprint

Context free grammars
Context-free Grammar
Grammar
Normal Form
Decision problem
Polynomials
Context free languages
Context-free Languages
Closure Properties
Countable
Polynomial time
Language
Polynomial
Integer

Keywords

  • Context-free languages of countable words
  • Countable words
  • Müller acceptance condition
  • Quasi-dense and dense words
  • Scattered
  • Well-ordered

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

On Müller context-free grammars. / Ésik, Z.; Iván, Szabolcs.

In: Theoretical Computer Science, Vol. 416, 27.01.2012, p. 17-32.

Research output: Contribution to journalArticle

Ésik, Z. ; Iván, Szabolcs. / On Müller context-free grammars. In: Theoretical Computer Science. 2012 ; Vol. 416. pp. 17-32.
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