Detecting palindromes, patterns and borders in regular languages

Authors:
Terry Anderson;John Loftus;Narad Rampersad;Nicolae Santean;Jeffrey Shallit
Affiliations:
School of Computer Science, University of Waterloo, Waterloo, Ont., Canada N2L 3G1;Luzerne County Community College, 1333 South Prospect Street, Nanticoke, PA 18634, USA;School of Computer Science, University of Waterloo, Waterloo, Ont., Canada N2L 3G1;School of Computer Science, University of Waterloo, Waterloo, Ont., Canada N2L 3G1;School of Computer Science, University of Waterloo, Waterloo, Ont., Canada N2L 3G1
Venue:
Information and Computation
Year:
2009

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Abstract

Given a language L and a non-deterministic finite automaton M, we consider whether we can determine efficiently (in the size of M) if M accepts at least one word in L, or infinitely many words. Given that M accepts at least one word in L, we consider how long a shortest word can be. The languages L that we examine include the palindromes, the non-palindromes, the k-powers, the non-k-powers, the powers, the non-powers (also called primitive words), the words matching a general pattern, the bordered words, and the unbordered words.