Rough Set Approximations of Languages

  • Authors:

  • Gheorghe P$\check{A}$un;Lech Polkowski;Andrzej Skowron

  • Affiliations:

  • (Work supported by the Academy of Finland, Project 11281, and the Polish Committee for Scientific Research, KBN, Grant 8T11C01011) Institute of Mathematics of the Romanian Academy, PO Box 1 - 764, ...;(Work supported by the Polish Committee for Scientific Research, KBN, Grant 8T11C01011) Institute of Mathematics, Warsaw University of Technology, Pl. Politechniki 1, 00-650 Warsaw, Poland. e-mail ...;(Work supported by the Polish Committee for Scientific Research, KBN, Grant 8T11C01011) Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warsaw, Poland. e-mail: skowron@mimuw.edu.pl

  • Venue:
  • Fundamenta Informaticae
  • Year:
  • 1997

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Abstract

We investigate here the possibility of approximating a language starting from a partial knowledge of its strings. This is understood as the possibility to read only a bounded part of a string: a prefix or a subword. In this way, indiscernibility relations among strings (they are equivalence or tolerance relations) are introduced, which lead to lower and upper approximations of languages. By varying the length of the perceived substring, we get sequences of approximations converging to the language. In many cases, the approximations of context-free languages are proved to be regular languages.