On Müller Context-Free Grammars

Ésik, Zoltán; Iván, Szabolcs

doi:10.1007/978-3-642-14455-4_17

Cited by 7 publications

(21 citation statements)

References 15 publications

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“…It is not difficult to see that a language L ⊆ A * is a BCFL iff it is an MCFL iff it is an ordinary context-free language (CFL), cf. [26,27]. On the other hand, there exists an MCFL that is not a BCFL, for example the set of all well-ordered words over a one-letter alphabet, cf.…”

Section: Context-free Languagesmentioning

confidence: 99%

“…We recall from [27] that a nonterminal X of an MCFG G = (N, A, R, S, F ) is reproductive if there is a word p ∈ (N ∪ A) ♯ containing an infinite number of occurrences of X with X ⇒ ∞ p. We call G non-reproductive if it has no reproductive nonterminal.…”

Section: Context-free Languages Of Scattered Words Of Bounded Rankmentioning

confidence: 99%

“…Context-free grammars generating arbitrary countable words were defined in [26,27]. Actually, two types of grammars were defined, context-free grammars with Büchi acceptance condition (BCFG), and context-free grammars with Muller acceptance condition (MCFG).…”

Section: Introductionmentioning

confidence: 99%

“…These grammars generate the Büchi and the Muller context-free languages of countable words, abbreviated as BCFLs and MCFLs. It is clear from the definitions in [26,27] that every BCFL is an MCFL. On the other hand, there exist MCFLs of even well-ordered words that are not BCFLs, for example the set of all countable well-ordered words over some alphabet.…”

Section: Introductionmentioning

confidence: 99%

“…More generally, it was shown in [26] that for every BCFL L of scattered words there is an integer n such that the Hausdorff rank of every word in L is bounded by n. On the other hand, regarding MCFLs L of scattered words, two cases arise, cf. [27]. Either there exists an integer n such that the rank of every word in L is bounded by n, or for every countable ordinal α there is a word in L whose Hausdorff rank exceeds α.…”

Section: Introductionmentioning

confidence: 99%

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On Context-Free Languages of Scattered Words

Ésik

Okawa

2013

Int. J. Found. Comput. Sci.

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It is known that if a Büchi context-free language (BCFL) consists of scattered words, then there is an integer n, depending only on the language, such that the Hausdorff rank of each word in the language is bounded by n. Every BCFL is a Muller context-free language (MCFL). In the first part of the paper, we prove that an MCFL of scattered words is a BCFL iff the rank of every word in the language is bounded by an integer depending only on the language.Then we establish operational characterizations of the BCFLs of well-ordered and scattered words. We prove that a language is a BCFL consisting of well-ordered words iff it can be generated from the singleton languages containing the letters of the alphabet by substitution into ordinary context-free languages and the ω-power operation. We also establish a corresponding result for BCFLs of scattered words and define expressions denoting BCFLs of well-ordered and scattered words. In the final part of the paper we give some applications.

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Section: Context-free Languagesmentioning

confidence: 99%

Section: Context-free Languages Of Scattered Words Of Bounded Rankmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On Context-Free Languages of Scattered Words

Ésik

Okawa

2013

Int. J. Found. Comput. Sci.

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Hausdorff Rank of Scattered Context-Free Linear Orders

Ésik

Iván

2012

LATIN 2012: Theoretical Informatics

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On Context-Free Languages of Scattered Words

Ésik

Okawa

2012

Developments in Language Theory

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It is known that if a Büchi context-free language (BCFL) consists of scattered words, then there is an integer n, depending only on the language, such that the Hausdorff rank of each word in the language is bounded by n. Every BCFL is a Müller context-free language (MCFL). In the first part of the paper, we prove that an MCFL of scattered words is a BCFL iff the rank of every word in the language is bounded by an integer depending only on the language.Then we establish operational characterizations of the BCFLs of well-ordered and scattered words. We prove that a language is a BCFL consisting of well-ordered words iff it can be generated from the singleton languages containing the letters of the alphabet by substitution into ordinary context-free languages and the ω-power operation. We also establish a corresponding result for BCFLs of scattered words and define expressions denoting BCFLs of well-ordered and scattered words. In the final part of the paper we give some applications.

show abstract

On Müller Context-Free Grammars

Cited by 7 publications

References 15 publications

On Context-Free Languages of Scattered Words

On Context-Free Languages of Scattered Words

Hausdorff Rank of Scattered Context-Free Linear Orders

On Context-Free Languages of Scattered Words

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