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Low Disruption Transformations on Cyclic Automata

Martin G.M., Vico F.J., Dassow J., Truthe B.

Fundamenta Informaticae

2010

Vol. 104, nr 1/2

93-110

We extend the edit operators of substitution, deletion, and insertion of a symbol over an word by introducing two new operators (partial copy and partial elimination) inspired by biological gene duplication. We define a disruption measure for an operator over a word and prove that whereas the traditional edit operators are disruptive, partial copy and partial elimination are non-disruptive. Moreover, we show that the application of only edit operators does not generate (with low disruption) all the words over a binary alphabet, but this can indeed be done by combining partial copy and partial elimination with the substitution operator.

A Similarity Measure for Cyclic Unary Regular Languages

Dassow J., Martin G.M., Vico F.J.

Fundamenta Informaticae

2009

Vol. 96, nr 1/2

71-88

A cyclic unary regular language is a regular language over a unary alphabet that is represented by a cyclic automaton. We propose a similarity measure for cyclic unary regular languages by modifying the Jaccard similarity coefficient and the Sorensen coefficient to measure the level of overlap between such languages. This measure computes the proportion of strings that are shared by two or more cyclic unary regular languages and is an upper bound of the Jaccard coefficient and the Sorensen coefficient. By using such similarity measure, we define a dissimilarity measure for cyclic unary regular languages that is a semimetric distance. Moreover, it can be used for the non-cyclic case.