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An Effective Algorithm for the Futile Questioning Problem

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Abstract

In the futile questioning problem, one must decide whether acquisition of additional information can possibly lead to the proof of a conclusion. Solution of that problem demands evaluation of a quantified Boolean formula at the second level of the polynomial hierarchy. The same evaluation problem, called Q-ALL SAT, arises in many other applications. In this paper, we introduce a special subclass of Q-ALL SAT that is at the first level of the polynomial hierarchy. We develop a solution algorithm for the general case that uses a backtracking search and a new form of learning of clauses. Results are reported for two sets of instances involving a robot route problem and a game problem. For these instances, the algorithm is substantially faster than state-of-the-art solvers for quantified Boolean formulas.

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Correspondence to Anja Remshagen.

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Remshagen, A., Truemper, K. An Effective Algorithm for the Futile Questioning Problem. J Autom Reasoning 34, 31–47 (2005). https://doi.org/10.1007/s10817-005-0981-8

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  • DOI: https://doi.org/10.1007/s10817-005-0981-8

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