Handbook of formal languages, vol. 1
Handbook of formal languages, vol. 1
Rough set approximations of languages
Fundamenta Informaticae - Special issue: to the memory of Prof. Cecylia Rauszer
Inductive Inference: Theory and Methods
ACM Computing Surveys (CSUR)
Rough Sets: Theoretical Aspects of Reasoning about Data
Rough Sets: Theoretical Aspects of Reasoning about Data
Automata, Languages, and Machines
Automata, Languages, and Machines
Automata, Languages, and Machines
Automata, Languages, and Machines
Incomplete Information: Rough Set Analysis
Incomplete Information: Rough Set Analysis
Automata and Computability
Varieties Of Formal Languages
Rough Sets: Mathematical Foundations
Rough Sets: Mathematical Foundations
Classification of regular languages by congruences
Classification of regular languages by congruences
Counter-Free Automata (M.I.T. research monograph no. 65)
Counter-Free Automata (M.I.T. research monograph no. 65)
On the existence of regular approximations
Theoretical Computer Science
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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.