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- W2039409656 abstract "It is known that $AM = BP cdot NP$. Babai [Proc. 17th Annual ACM Symposium Theory of Computing, 1985, pp. 421–429] and Goldwasser and Sipser [Proc.18th Annual ACM Symposium on Theory of Computing, 1986, pp. 59–68] asked whether $BP cdot NP{text{ for almost every set }}B,A in NP(B)}$ is equal to ${ A|$ . This question is still open. In this paper it is shown that (1) for every $k geqq 0$ and every set $A,A in BP cdot Sigma _k^P $ if and only if for almost every tally set , and (2) for every $k geqq 0$ and almost every tally set $T,BP cdot Sigma _k^P (T) = Sigma _k^P (T)$. From them are obtained some properties of the “BP-polynomial-time hierarchy” studied by Schoning [Proc. 2nd Annual Conference on Structure in Complexity Theory, 1987, pp. 2–8]. That is, the $BP$-polynomial-time hierarchy has the properties that are precisely parallel to those of the polynomial-time hierarchy. The proofs of these results provide examples of the use of properties of complexity classes specified by relativizations to obtain properties of unrelativized complexity classes." @default.
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- W2039409656 date "1989-06-01" @default.
- W2039409656 modified "2023-09-23" @default.
- W2039409656 title "On Tally Relativizations of $BP$-Complexity Classes" @default.
- W2039409656 doi "https://doi.org/10.1137/0218031" @default.
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