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• W2050190588 abstract "In this paper, we investigate relative complexity between #P and other classes of functions. Our particular interest is to compare #P with #PH and with PFH by using polynomial-time reducibility and to demonstrate that a weaker notion of polynomial-time reducibility is sufficiently powerful for reducing #PH functions to #P functions. Our main result is stated as follows: Every function in #PH is polynomial-time 1-Turing reducible to some function in #P. That is, # PH ⊆ PF # P [1] . Some consequences of this result are as follows: Every function in PFH is polynomial-time 1-Turing reducible to some function in #P. If PF # P [1] ⊆# PH , then PH collapses to a finite level; furthermore, if either # P ⊆ PFH or PFH ⊆# P , then PH collapses to a finite level. We also give an affirmative answer to an open question posed by Valiant (1979), and we show a generalized result about p-rankability by Hemachandra (1987)." @default.
• W2050190588 created "2016-06-24" @default.
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• W2050190588 date "1992-06-01" @default.
• W2050190588 modified "2023-09-26" @default.
• W2050190588 title "Polynomial-time 1-Turing reductions from #PH to #P" @default.
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• W2050190588 doi "https://doi.org/10.1016/0304-3975(92)90369-q" @default.
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