<P> Decision problems can be ordered according to many - one reducibility and related to feasible reductions such as polynomial - time reductions . A decision problem P is said to be complete for a set of decision problems S if P is a member of S and every problem in S can be reduced to P. Complete decision problems are used in computational complexity to characterize complexity classes of decision problems . For example, the Boolean satisfiability problem is complete for the class NP of decision problems under polynomial - time reducibility . </P> <P> Decision problems are closely related to function problems, which can have answers that are more complex than a simple' yes' or' no' . A corresponding function problem is "given two numbers x and y, what is x divided by y?". </P> <P> A function problem consists of a partial function f; the informal "problem" is to compute the values of f on the inputs for which it is defined . </P> <P> Every function problem can be turned into a decision problem; the decision problem is just the graph of the associated function . (The graph of a function f is the set of pairs (x, y) such that f (x) = y .) If this decision problem were effectively solvable then the function problem would be as well . This reduction does not respect computational complexity, however . For example, it is possible for the graph of a function to be decidable in polynomial time (in which case running time is computed as a function of the pair (x, y)) when the function is not computable in polynomial time (in which case running time is computed as a function of x alone). The function f (x) = 2 has this property . </P>

When is a decision problem said to be polynomially reversible