Problems in The Polynomial Hierarchy
- An example of a natural problem in is circuit minimization: given a number k and a circuit A computing a Boolean function f, determine if there is a circuit with at most k gates that computes the same function f. Let be the set of all boolean circuits. The language
- A complete problem for is satisfiability for quantified Boolean formulas with k alternations of quantifiers (abbreviated QBFk or QSATk). This is the version of the boolean satisfiability problem for . In this problem, we are given a Boolean formula f with variables partitioned into k sets X1, ..., Xk. We have to determine if it is true that
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