Regular patterns, regular languages and context-free languages

Authors:
Sanjay Jain;Yuh Shin Ong;Frank Stephan
Affiliations:
Department of Computer Science, National University of Singapore, Singapore 117417, Republic of Singapore;Department of Computer Science, National University of Singapore, Singapore 117417, Republic of Singapore;Department of Mathematics, National University of Singapore, Singapore 119076, Republic of Singapore
Venue:
Information Processing Letters
Year:
2010

Citing 11
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Abstract

In this paper we consider two questions. First we consider whether every pattern language which is regular can be generated by a regular pattern. We show that this is indeed the case for extended (erasing) pattern languages if alphabet size is at least four. In all other cases, we show that there are patterns generating a regular language which cannot be generated by a regular pattern. Next we consider whether there are pattern languages which are context-free but not regular. We show that, for alphabet size 2 and 3, there are both erasing and non-erasing pattern languages which are context-free but not regular. On the other hand, for alphabet size at least 4, every erasing pattern language which is context-free is also regular. It is open at present whether there exist non-erasing pattern languages which are context-free but not regular for alphabet size at least 4.