Abstract

We continue the study of combinatorial property testing, initiated by Goldreich, Goldwasser and Ron in [7]. The subject of this paper is testing regular languages. Our main result is as follows. For a regular language L 2 f0; 1g and an integer n there exists a randomized algorithm which always accepts a word w of length n if w 2 L, and rejects it with high probability if w has to be modified in at least n positions to create a word in L. The algorithm queries ~ O(1=) bits of w. This query complexity is shown to be optimal up to a factor poly-logarithmic in 1=. We also discuss testability of more complex languages and show, in particular, that the query complexity required for testing contextfree languages cannot be bounded by any function of . The problem of testing regular languages can be viewed as a part of a very general approach, seeking to probe testability of properties defined by logical means. 1

Citations