Monotonicity testing over general poset domains
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Testing membership in parenthesis languages
Random Structures & Algorithms
Testing subgraphs in large graphs
Random Structures & Algorithms - Special issue: Proceedings of the tenth international conference "Random structures and algorithms"
Some 3CNF properties are hard to test
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Testing subgraphs in directed graphs
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Functions that have read-once branching programs of quadratic size are not necessarily testable
Information Processing Letters
On the strength of comparisons in property testing
Information and Computation
A characterization of easily testable induced subgraphs
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Functions that have read-twice constant width branching programs are not necessarily testable
Random Structures & Algorithms
Every monotone graph property is testable
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
A large lower bound on the query complexity of a simple boolean function
Information Processing Letters
A Characterization of the (natural) Graph Properties Testable with One-Sided Error
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
A combinatorial characterization of the testable graph properties: it's all about regularity
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Space Complexity Vs. Query Complexity
Computational Complexity
Approximate schemas, source-consistency and query answering
Journal of Intelligent Information Systems
Property Testing: A Learning Theory Perspective
Foundations and Trends® in Machine Learning
A large lower bound on the query complexity of a simple boolean function
Information Processing Letters
Algorithmic and Analysis Techniques in Property Testing
Foundations and Trends® in Theoretical Computer Science
Testing convexity properties of tree colorings
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Indistinguishability and first-order logic
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
Recognizing well-parenthesized expressions in the streaming model
Proceedings of the forty-second ACM symposium on Theory of computing
Relational properties expressible with one universal quantifier are testable
SAGA'09 Proceedings of the 5th international conference on Stochastic algorithms: foundations and applications
Lower bounds for testing triangle-freeness in Boolean functions
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
On testing computability by small width OBDDs
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Approximate Satisfiability and Equivalence
SIAM Journal on Computing
Property testing of massively parametrized problems – a survey
Property testing
Property testing of massively parametrized problems – a survey
Property testing
Testing permutation properties through subpermutations
Theoretical Computer Science
Untestable properties in the kahr-moore-wang class
WoLLIC'11 Proceedings of the 18th international conference on Logic, language, information and computation
Streaming algorithms for recognizing nearly well-parenthesized expressions
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
ICDT'07 Proceedings of the 11th international conference on Database Theory
Property testing and the branching program size of boolean functions
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
Space complexity vs. query complexity
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
Testable and untestable classes of first-order formulae
Journal of Computer and System Sciences
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
Partial tests, universal tests and decomposability
Proceedings of the 5th conference on Innovations in theoretical computer science
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We continue the study of combinatorial property testing, initiated by Goldreich, 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 $L\in \{0,1\}^*$ and an integer n there exists a randomized algorithm which always accepts a word w of length n if $w\in L$ and rejects it with high probability if $w$ has to be modified in at least $\epsilon n$ positions to create a word in L. The algorithm queries $\tilde{O}(1/\epsilon)$ bits of w. This query complexity is shown to be optimal up to a factor polylogarithmic in $1/\epsilon$. We also discuss the 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.