The algorithmic aspects of the regularity lemma
Journal of Algorithms
Some optimal inapproximability results
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
Random sampling and approximation of MAX-CSP problems
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
SIAM Journal on Discrete Mathematics
Property testers for dense constraint satisfaction programs on finite domains
Random Structures & Algorithms
Testing subgraphs in directed graphs
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
A 7/8-Approximation Algorithm for MAX 3SAT?
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
Testing Subgraphs in Large Graphs
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
A characterization of easily testable induced subgraphs
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Every monotone graph property is testable
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Testing hypergraph colorability
Theoretical Computer Science - Automata, languages and programming
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
Property Testing: A Learning Theory Perspective
Foundations and Trends® in Machine Learning
Algorithmic and Analysis Techniques in Property Testing
Foundations and Trends® in Theoretical Computer Science
Testing permutation properties through subpermutations
Theoretical Computer Science
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Let φ be a set of general boolean functions on n variables, such that each function depends on exactly k variables, and each variable can take a value from [1, d]. We say that φ is ε-far from satisfiable, if one must remove at least εnk functions in order to make the set of remaining functions satisfiable. Our main result is that if φ is ε-far from satisfiable, then most of the induced, sets of functions, on sets of variables of size c(k, d)/ε2, are not satisfiable, where c(k, d) depends only on k and d. Using the above claim, we obtain similar results for k-SAT and k-NAEQ-SAT.Assume we relax the decision problem of whether an instance of one of the above mentioned problems is satisfiable or not, to the problem of deciding whether an instance is satisfiable or ε-far from satisfiable. While the above decision problems are NP-hard, our result implies that we can solve their relaxed versions, that is, distinguishing between satisfiable and ε-far from satisfiable instances, in randomized constant time.From the above result we obtain as a special case, previous results of Alon and Krivelevich, and of Czumaj and Sohler, concerning testing of graphs and hypergraphs colorability. We also discuss the difference between testing with one-sided and two-sided error.