Rough Approximations in Varieties of Regular Languages

Article type: Research Article

Authors: Martin, Gabriela | Steinby, Magnus

Affiliations: Research Group on Mathematical Linguistics, Rovira i Virgili University, Spain. gabrielasusana.martin@estudiants.urv.es | Department of Mathematics and Turku Centre for Computer Science, University of Turku, Finland. steinby@utu.fi

Note: [] Address for correspondence: Department of Mathematics, University of Turku, FI-20014 Turku, Finland

Abstract: We study approximations of regular languages bymembers of a given variety ℒ of regular languages. These are upper or lower approximations in the sense of Pawlak's rough set theory with respect to congruences belonging to the variety of congruences corresponding to ℒ. In particular, we consider the closest upper and lower approximations in ℒ. In so-called principal varieties these always exist, and we present algorithms for finding them, but for other varieties the situation is more complex. Although we consider just Eilenberg’s +-varieties, the general ideas apply also to other types of varieties of languages. Our work may also be viewed as an approach to the characterizable inference problem in which a language of a certain kind is to be inferred from a given sample.

Keywords: Regular languages, rough approximations, varieties of languages, finite automata

DOI: 10.3233/FI-2011-591

Journal: Fundamenta Informaticae, vol. 112, no. 4, pp. 281-303, 2011