40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039) (1999)
New York, New York
Oct. 17, 1999 to Oct. 18, 1999
Noga Alon , Tel Aviv University
Michael Krivelevich , Rutgers University
Ilan Newman , University of Haifa
Mario Szegedy , AT&T Labs-Research
We continue the study of combinatorial property testing, initiated by Goldreich, Goldwasser and Ron in 1996. The subject of this paper is testing regular languages. Our main result is as follows. For a regular language L over the binary alphabet, an integer n and a small enough constant \math, there exists a randomized algorithm which always accepts a word w of length n if w belongs to L, and rejects it with high probability if w has to be modified in at least \math positions to create a word in L. The algorithm queries \math polylog \math bits of w. This query complexity is shown to be optimal up to a factor poly-logarithmic in \math. We also discuss testability of more complex languages and show, in particular, that the query complexity required for testing context-free languages cannot be bounded by any function of epsilon. 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.
regular languages, randomized algorithms, testing
M. Krivelevich, N. Alon, M. Szegedy and I. Newman, "Regular Languages are Testable with a Constant Number of Queries," 40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039)(FOCS), New York, New York, 1999, pp. 645.