A Taxonomy of Complexity Classes of Functions (1992)
| Venue: | Journal of Computer and System Sciences |
| Citations: | 82 - 12 self |
BibTeX
@ARTICLE{Selman92ataxonomy,
author = {Alan L. Selman and Fewpf Pf},
title = {A Taxonomy of Complexity Classes of Functions},
journal = {Journal of Computer and System Sciences},
year = {1992},
volume = {48},
pages = {357--381}
}
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Abstract
This paper comprises a systematic comparison of several complexity classes of functions that are computed nondeterministically in polynomial time or with an oracle in NP. There are three components to this work. ffl A taxonomy is presented that demonstrates all known inclusion relations of these classes. For (nearly) each inclusion that is not shown to hold, evidence is presented to indicate that the inclusion is false. As an example, consider FewPF, the class of multivalued functions that are nondeterministically computable in polynomial time such that for each x, there is a polynomial bound on the number of distinct output values of f(x). We show that FewPF ` PF NP tt . However, we show PF NP tt ` FewPF if and only if NP = co-NP, and thus PF NP tt ` FewPF is likely to be false. ffl Whereas it is known that P NP (O(log n)) = P NP tt ` P NP [Hem87, Wagb, BH88], we show that PF NP (O(log n)) = PF NP tt implies P = FewP and R = NP. Also, we show that PF NP tt = PF ...
