Regular languages are testable with a constant number of queries

Noga Mordechai Alon, Michael Krivelevich, Ilan Newman, Mario Szegedy

Research output: Contribution to journalConference article

29 Scopus citations

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 qq {0.1}* and an integer n there exists a randomized algorithm which always accepts a word w of length n if w qq L, and rejects it with high probability if w has to be modified in at least qqn positions to create a word on L. The algorithm queries qq(1/qq) bits of w. This query complexity is shown to be optimal up to a factory poly-logarithmic in 1/qq. 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 qq. 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.

Original languageEnglish (US)
Pages (from-to)645-655
Number of pages11
JournalAnnual Symposium on Foundations of Computer Science - Proceedings
StatePublished - Jan 1 1999
Externally publishedYes
EventProceedings of the 1999 IEEE 40th Annual Conference on Foundations of Computer Science - New York, NY, USA
Duration: Oct 17 1999Oct 19 1999

All Science Journal Classification (ASJC) codes

  • Hardware and Architecture

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