From Pebble Games to Tractability: An Ambidextrous Consistency Algorithm for Quantified Constraint Satisfaction

The constraint satisfaction problem (CSP) and quantified constraint satisfaction problem (QCSP) are common frameworks for the modelling of computational problems. Although they are intractable in general, a rich line of research has identified restricted cases of these problems that are tractable in polynomial time. Remarkably, many tractable cases of the CSP that have been identified are solvable by a single algorithm, which we call here the consistency algorithm. In this paper, we give a natural extension of the consistency algorithm to the QCSP setting, by making use of connections between the consistency algorithm and certain two-person pebble games. Surprisingly, we demonstrate a variety of tractability results using the algorithm, revealing unified structure among apparently different cases of the QCSP.

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