A Similarity Measure for Cyclic Unary Regular Languages

  • Authors:
  • Jü/rgen Dassow;Gema M. Martí/n;Francisco J. Vico

  • Affiliations:
  • Otto-von-Guericke-Universitä/tMagdeburg, Fakultä/t fü/r Informatik, PSF 4120, D-39016 Magdeburg, Germany. E-mail: dassow@iws.cs.uni-magdeburg.de;Departamento de Lenguajes y Ciencias de la Computació/n, Universidad de Má/laga Severo Ochoa, 4, Parque Tecnoló/gico de Andalucí/e/a, E-29590 Campanillas - Má/laga, Spain. E-ma ...;Departamento de Lenguajes y Ciencias de la Computació/n, Universidad de Má/laga Severo Ochoa, 4, Parque Tecnoló/gico de Andalucí/e/a, E-29590 Campanillas - Má/laga, Spain. E-ma ...

  • Venue:
  • Fundamenta Informaticae
  • Year:
  • 2009

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Abstract

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 Sørensen 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 Sørensen 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.