Complexity of generalized satisfiability counting problems
Information and Computation
On the algebraic structure of combinatorial problems
Theoretical Computer Science
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
Monotonicity testing over general poset domains
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Robust Characterizations of Polynomials withApplications to Program Testing
SIAM Journal on Computing
Constraint Satisfaction Problems and Finite Algebras
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Some 3CNF Properties Are Hard to Test
SIAM Journal on Computing
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
Graph limits and parameter testing
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
The complexity of homomorphism and constraint satisfaction problems seen from the other side
Journal of the ACM (JACM)
A Characterization of the (Natural) Graph Properties Testable with One-Sided Error
SIAM Journal on Computing
Algebraic property testing: the role of invariance
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Undirected connectivity in log-space
Journal of the ACM (JACM)
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
The complexity of satisfiability problems: Refining Schaefer's theorem
Journal of Computer and System Sciences
A Unified Framework for Testing Linear-Invariant Properties
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Property testing of massively parametrized problems – a survey
Property testing
CCC '12 Proceedings of the 2012 IEEE Conference on Computational Complexity (CCC)
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Given an instance $\mathcal{I}$ of a CSP, a tester for $\mathcal{I}$ distinguishes assignments satisfying $\mathcal{I}$ from those which are far from any assignment satisfying $\mathcal{I}$. The efficiency of a tester is measured by its query complexity, the number of variable assignments queried by the algorithm. In this paper, we characterize the hardness of testing Boolean CSPs in terms of the algebra generated by the relations used to form constraints. In terms of computational complexity, we show that if a non-trivial Boolean CSP is sublinear-query testable (resp., not sublinear-query testable), then the CSP is in NL (resp., P-complete, ⊕L-complete or NL-complete) and that if a sublinear-query testable Boolean CSP is constant-query testable (resp., not constant-query testable), then counting the number of solutions of the CSP is in P (resp., $\sharp$P-complete). Also, we conjecture that a CSP instance is testable in sublinear time if its Gaifman graph has bounded treewidth. We confirm the conjecture when a near-unanimity operation is a polymorphism of the CSP.