Finite Automata, Palindromes, Powers, and Patterns

  • Authors:

  • Terry Anderson;Narad Rampersad;Nicolae Santean;Jeffrey Shallit

  • Affiliations:

  • David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, Canada N2L 3G1;David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, Canada N2L 3G1;David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, Canada N2L 3G1;David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, Canada N2L 3G1

  • Venue:
  • Language and Automata Theory and Applications
  • Year:
  • 2008

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Abstract

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