On locally reversible languages

Authors:
Pedro García;Manuel Vázquez de Parga;Antonio Cano;Damián López
Affiliations:
Departamento de Sistemas Informáticos y Computación, Universidad Politécnica de Valencia, Camino de Vera s/n, 46071, Valencia, Spain;Departamento de Sistemas Informáticos y Computación, Universidad Politécnica de Valencia, Camino de Vera s/n, 46071, Valencia, Spain;Departamento de Sistemas Informáticos y Computación, Universidad Politécnica de Valencia, Camino de Vera s/n, 46071, Valencia, Spain;Departamento de Sistemas Informáticos y Computación, Universidad Politécnica de Valencia, Camino de Vera s/n, 46071, Valencia, Spain
Venue:
Theoretical Computer Science
Year:
2009

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Abstract

There exist several works that study the class of reversible languages defined as the union closure of 0-reversible languages, their properties and suitable representations. In this work we define and study the class of locally reversible languages, defined as the union closure of k-reversible languages. We characterize the class and prove that it is a local (positive) variety of formal languages. We also extend the definition of quasi-reversible automata to deal with locally reversible languages and propose a polynomial algorithm to obtain, for any given locally k-reversible language, a quasi-k-reversible automaton.