Abstract
We introduce a general framework for the definition of function classes. Our model, which is based on nondeterministic polynomial-time Turing transducers, allows uniform characterizations of FP, FP NP , FP NP [O ( log n)], [Formula: see text], counting classes (#·P, #·NP, #·coNP, GapP, GapP NP ), optimization classes (max·P, min·P, max·NP, min·NP), promise classes (NPSV, # few · P , c #· P ), multivalued classes (FewFP, NPMV), and many more. Each such class is defined in our model by a scheme how to evaluate computation trees of nondeterministic machines. We study a reducibility notion between such evaluation schemes, which leads to a necessary and sufficient criterion for relativizable inclusion between function classes. As it turns out, this criterion is easily applicable and we get as a consequence, e.g., that there is an oracle A, such that min · P A⊈#· NP A (note that no structural consequences are known to follow from the corresponding positive inclusion).
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