Undecidable problems concerning densities of languages

In this paper we prove that the question whether a language presented by a context free grammar has density, is undecidable. Moreover we show that there is no algorithm which, given two unambiguous context free grammars on input, decides whether the language defined by the first grammar has a relati...

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Published in:Discrete mathematics and theoretical computer science Vol. DMTCS Proceedings vol. AF,...; no. Proceedings; pp. 69 - 76
Main Author: Kozik, Jakub
Format: Journal Article Conference Proceeding
Language:English
Published: DMTCS 01.01.2005
Discrete Mathematics and Theoretical Computer Science
Discrete Mathematics & Theoretical Computer Science
Series:DMTCS Proceedings
Subjects:
[info.info-lo] computer science [cs]/logic in computer science [cs.lo]
[info.info-sc] computer science [cs]/symbolic computation [cs.sc]
asymptotic density
Computer Science
context-free languages
decidability
Logic in Computer Science
Symbolic Computation
decidability
context-free languages
asymptotic density
ISSN:1365-8050, 1462-7264, 1365-8050
Online Access:Get full text
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Abstract In this paper we prove that the question whether a language presented by a context free grammar has density, is undecidable. Moreover we show that there is no algorithm which, given two unambiguous context free grammars on input, decides whether the language defined by the first grammar has a relative density in the language defined by the second one. Our techniques can be extended to show that this problem is undecidable even for languages given by grammars from $LL(k)$ (for sufficiently large fixed $k ∈ \mathbb{N} )$.
AbstractList In this paper we prove that the question whether a language presented by a context free grammar has density, is undecidable. Moreover we show that there is no algorithm which, given two unambiguous context free grammars on input, decides whether the language defined by the first grammar has a relative density in the language defined by the second one. Our techniques can be extended to show that this problem is undecidable even for languages given by grammars from $LL(k)$ (for sufficiently large fixed $k ∈ \mathbb{N} )$.
Author Kozik, Jakub
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Keywords decidability
context-free languages
asymptotic density
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Snippet In this paper we prove that the question whether a language presented by a context free grammar has density, is undecidable. Moreover we show that there is no...
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SubjectTerms [info.info-lo] computer science [cs]/logic in computer science [cs.lo]
[info.info-sc] computer science [cs]/symbolic computation [cs.sc]
asymptotic density
Computer Science
context-free languages
decidability
Logic in Computer Science
Symbolic Computation
Title Undecidable problems concerning densities of languages
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