Property testers for dense constraint satisfaction programs on finite domains

Authors:
Gunnar Andersson;Lars Engebretsen
Affiliations:
Prover Technology, Alströmergatan 22, SE-112 47 Stockholm, Sweden;Department of Numerical Analysis and Computer Science, Royal Institute of Technology, SE-100 44 Stockholm, Sweden
Venue:
Random Structures & Algorithms
Year:
2002

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Abstract

Many NP-hard languages can be "decided" in subexponential time if the definition of "decide" is relaxed only slightly. Rubinfeld and Sudan introduced the notion of property testers, probabilistic algorithms that can decide, with high probability, if a function has a certain property or if it is far from any function having this property. Goldreich, Goldwasser, and Ron constructed property testers with constant query complexity for dense instances of a large class of graph problems. Since many graph problems can be viewed as special cases of the Constraint Satisfaction Problem on Boolean domains, it is natural to try to construct property testers for more general cases of the Constraint Satisfaction Problem. In this paper, we give explicit constructions of property testers using a constant number of queries for dense instances of Constraint Satisfaction Problems where the constraints have constant arity and the variables assume values in some domain of finite size.