Regular and context-free pattern languages over small alphabets

Authors:
Daniel Reidenbach;Markus L. Schmid
Affiliations:
Department of Computer Science, Loughborough University, Loughborough, Leicestershire, United Kingdom;Department of Computer Science, Loughborough University, Loughborough, Leicestershire, United Kingdom
Venue:
DLT'12 Proceedings of the 16th international conference on Developments in Language Theory
Year:
2012

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Regular and context-free pattern languages over small alphabets

Theoretical Computer Science

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Abstract

Pattern languages are generalisations of the copy language, which is a standard textbook example of a context-sensitive and non-context-free language. In this work, we investigate a counter-intuitive phenomenon: with respect to alphabets of size 2 and 3, pattern languages can be regular or context-free in an unexpected way. For this regularity and context-freeness of pattern languages, we give several sufficient and necessary conditions and improve known results.