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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“If family communication is good, parents can pick up the signs of stress in children and talk about it before it results in some crisis. If family communication is bad, not only will parents be insensitive to potential crises, but the poor communication will contribute to problems in the family.”
—Donald C. Medeiros (20th century)
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