A relation by palindromic subwords

Authors:
Mark Daley;Kalpana Mahalingam
Affiliations:
Department of Computer Science and Department of Biology, University of Western Ontario, London, Canada N6A 5B7;Department of Mathematics, Indian Institute of Technology, Chennai, India 600 042
Venue:
Natural Computing: an international journal
Year:
2010

Citing 4
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MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
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DNA13'07 Proceedings of the 13th international conference on DNA computing
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Natural Computing: an international journal

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Abstract

We define a new relation on words by a finite series of insertions and/or deletions of palindromic subwords. In particular we concentrate on insertion or deletion of Watson---Crick palindromes. We show that the new relation ~驴 is, in fact, an equivalence relation where 驴 is any arbitrary antimorphic involution that is not the identity on the letters of the alphabet. We also show that the set of all 驴-palindromic free words defined in (Daley et al. in preparation) is ~驴-independent. Using the relation we define a new subclass of primitive words which we call as ~驴-primitive words and show that the class of all ~驴-primitive words is closed under circular permutations. We also define ~驴-conjugates and ~驴-commutativity and study the properties of such words and show that they are similar to that of conjugate words and words that commute.