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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Bibliographic Details
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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Summary: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 $k ∈ \mathbb{N} )$.
ISSN:1365-8050
1462-7264
1365-8050
DOI:10.46298/dmtcs.3471