Acceptor-definable counting classes
PCI'01 Proceedings of the 8th Panhellenic conference on Informatics
Functions Computable with Nonadaptive Queries to NP
Theory of Computing Systems
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PF( Hash P) is characterized in a manner similar to M.W. Krentel's (1988) characterization of Pf(NP). If MidP is the class of functions that give the medians in the outputs of metric Turing machines, then it is shown that every function in PF( Hash P) is polynomial time 1-Turing reducible to a function in MidP and MidP contained in PF( Hash P); that is, PF( Hash P)=PF(MidP(1)). Intuitively, finding medians is as hard computationally as PF( Hash P); this forms a contrast to an intuitive interpretation of Krentel's result that finding maxima (or minima) is as hard as PF(NP). Several applications of the result are shown.