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- W2170377962 abstract "By Bennet and Gill [4], it is shown that if A is a random oracle then TAUT / ∈ P with probability 1, where TAUT denotes the collection of all tautologies relative to A. Extending Dowd’s work [6], we present a forcing argument to bound execution time of a while-loop of a deterministic algorithm, by which we show that for each positive integer r, if A is an r-generic oracle in the sense of Dowd then rTAUT≡T TAUT ⊕ A, where rTAUT denotes the collection of all r-query tautologies with respect to A. As a consequence, the following two assertions are equivalent : (i) if A is a random oracle then rTAUT / ∈ P with probability 1, (ii) R 6= NP ." @default.
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- W2170377962 date "1998-12-01" @default.
- W2170377962 modified "2023-09-23" @default.
- W2170377962 title "Recognizing tautology by a deterministic algorithm whose while-loop's execution time is bounded by forcing" @default.
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