Ivanyos, Gábor and Kulkarni, R and Qiao, YM and Santha, M and Sundaram, A (2018) On the complexity of trial and error for constraint satisfaction problems. JOURNAL OF COMPUTER AND SYSTEM SCIENCES, 92. pp. 48-64. ISSN 0022-0000 10.1016/j.jcss.2017.07.005

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Abstract

In 2013 Bei, Chen and Zhang introduced a trial and error model of computing, and applied to some constraint satisfaction problems. In this model the input is hidden by an oracle which, for a candidate assignment, reveals some information about a violated constraint if the assignment is not satisfying. In this paper we initiate a systematic study of constraint satisfaction problems in the trial and error model, by adopting a formal framework for CSPs, and defining several types of revealing oracles. Our main contribution is to develop a transfer theorem for each type of the revealing oracle. To any hidden CSP with a specific type of revealing Oracle, the transfer theorem associates another CSP in the normal setting, such that their complexities are polynomial-time equivalent. This in principle transfers the study of a large class of hidden CSPs to the study of normal CSPs. We apply the transfer theorems to get polynomial-time algorithms or hardness results for several families of concrete problems. (C) 2017 Elsevier Inc. All rights reserved.

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