Testing Assignments of Boolean CSPs

Abstract

<lb>Given an instance I of a CSP, a tester for I distinguishes assignments satisfying I from<lb>those which are far from any assignment satisfying I. The efficiency of a tester is measured<lb>by its query complexity, the number of variable assignments queried by the algorithm. In this<lb>paper, we characterize the hardness of testing Boolean CSPs according to the relations used<lb>to form constraints. In terms of computational complexity, we show that if a Boolean CSP<lb>is sublinear-query testable (resp., not sublinear-query testable), then the CSP is in NL (resp.,<lb>P-complete, ⊕L-complete or NP-complete) and that if a sublinear-query testable Boolean CSP<lb>is constant-query testable (resp., not constant-query testable), then counting the number of<lb>solutions of the CSP is in P (resp., #P-complete). The classification is done by showing an Ω(n)<lb>lower bound for testing Horn 3-SAT and investigating Post’s lattice, the inclusion structure of<lb>Boolean algebras associated with CSPs.

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Cite this paper

@article{Bhattacharyya2012TestingAO, title={Testing Assignments of Boolean CSPs}, author={Arnab Bhattacharyya and Yuichi Yoshida}, journal={Electronic Colloquium on Computational Complexity (ECCC)}, year={2012}, volume={19}, pages={103} }