The Complexity of Futile Questioning

Instances of the futile questioning problem abound in applications, especially, in the area of artificial intelligence. The problem can be represented by a particular quantified Boolean formula. A variation of the problem includes also costs for the logic variables. Typically, the problem is simplified instead of solved directly, which may lead to inaccurate results. Alternatively, the problem can be transformed to a standard format. We investigate the complexity of the futile questioning problem and two subclasses. Based on the complexity result, we argue that a transformation to the standard format is not suitable for practical purposes.