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• W1992972561 abstract "Consider the following open problems: (i) ${text{P}} = ? {text{ NP}}$ (ii) ${text{NP}} = ? {text{ co-NP}}$; (iii) ${text{P}} = ? {text{ PSPACE}}$; (iv) ${text{NP}} = ? {text{ PSPACE}}$. In this paper we study these four problems from a particular point of view. To illustrate our approach, consider the first problem. It is known that there exist recursive sets A and B such that ${text{P}}(A) = {text{NP}}(A)$ and ${text{P}}(B) ne {text{NP}}(B)$. We study restrictions R on both the deterministic and also the nondeterministic polynomial time-bounded oracle machines such that the following holds: ${text{P}} = {text{NP}}$ if and only if for every set A, ${text{P}}_R (A) = {text{NP}}_R (A)$. The restrictions are “quantitative” in the sense that the size of the set of strings queried by the oracle in computations of a machine on an input is bounded by a polynomial in the length of the input. We study several different ways of specifying such quantitative restrictions, each of which has the desired property." @default.
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• W1992972561 date "1984-08-01" @default.
• W1992972561 modified "2023-09-27" @default.
• W1992972561 title "Quantitative Relativizations of Complexity Classes" @default.
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• W1992972561 doi "https://doi.org/10.1137/0213030" @default.
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