A duplication is basic phenomenon that occurs through molecular evolution on a biological sequence. A duplication on a string copies any substring of the string. We define k-pseudo-duplication of a string w that consists, roughly speaking, of all strings obtained from w by inserting after a substring u another substring obtained from u by at most k edit operations. We consider three variants of duplication operations, duplication, k-pseudo-duplication and reverse-duplication. First, we give the necessary and sufficient number of states that a nondeterministic finite automaton needs to recognize duplications on a string. Then, we show that regular languages and context-free languages are not closed under the duplication, k-pseudo-duplication and reverse-duplication operations. Furthermore, we show that the class of context-sensitive languages is closed under duplication, pseudo-duplication and reverse-duplication.
CITATION STYLE
Cho, D. J., Han, Y. S., Kim, H., Palioudakis, A., & Salomaa, K. (2015). Duplications and pseudo-duplications. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9252, pp. 157–168). Springer Verlag. https://doi.org/10.1007/978-3-319-21819-9_11
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