Regular languages are testable with a constant number of queries

We continue the study of combinatorial property testing, initiated by Goldr eich, Goldwasser, and Ron in [J. ACM, 45 (1998), pp. 653-750]. The subject of this paper is testing regular languages. Our main result is as follows. For a regular language L is an element of {0,1}* and an integer n there exi sts a randomized algorithm which always accepts a word w of length n if w i s an element of L and rejects it with high probability if w has to be modif ied in at least epsilonn positions to create a word in L. The algorithm que ries (O) over tilde (1/epsilon) bits of w. This query complexity is shown t o be optimal up to a factor polylogarithmic in 1/epsilon. We also discuss t he testability of more complex languages and show, in particular, that the query complexity required for testing context-free languages cannot be boun ded by any function of epsilon. The problem of testing regular languages ca n be viewed as a part of a very general approach, seeking to probe testabil ity of properties defined by logical means.