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A Similarity Measure for Cyclic Unary Regular Languages

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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.
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71--88
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Bibliogr. 18 poz.
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Bibliografia
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  • [10] Levi, A.: Basic Set Theory. Dover, 1979.
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  • [13] Pighizzini, G.: Unary Language Concatenation and Its State Complexity, in: Proceedings 5th International Conference on Implementation and Application of Automata, Lecture Notes in Computer Science 2088 (2001) 252-262.
  • [14] Pighizzini, G., Shallit, J.: Unary Language Operations, State Complexity and Jacobsthal's Function, Intl. J. Found. Comp. Sci. 13 (2002) 145-159.
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  • [18] Wikipedia articles on Jaccard coefficient and Sørensen coefficient.
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bwmeta1.element.baztech-article-BUS8-0008-0042
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