A note on some simultaneous relations among time, space, and reversal for single work tape nondeterministic turing machines

Q4 Mathematics 信息与控制 Pub Date : 1986-08-01 DOI:10.1016/S0019-9958(86)80003-1

Etsuro Moriya, Shigeki Iwata, Takumi Kasai

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引用次数: 3

Abstract

Simultaneous resource bounded complexity classes for nondeterministic single worktape off-line Turing machines are considered such as time-space bounded classes, denoted by NTISP₁(T, S), reversal-space bounded classes, denoted by NRESP₁(R, S), and time-reversal bounded classes, denoted by NTIRE₁(T, R). It is shown that NRESP₁(R(n), S(n)) contains NTISP₁(S(n), R(n)) and is contained in NTISP₁(R(n) S(n)n² log n, R(n) log n). The following corollaries follow: (1) the affirmative solution to the nondeterministic single worktape version of the NC = ? SC problem, NTIRE₁(poly, polylog) = NTISP₁(poly, polylog), and (2) a reversal-space trade-off, NRESP₁(polylog, poly) = NRESP₁(poly, polylog).

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单工作带不确定性图灵机的时间、空间和反转的同时关系

考虑不确定性单磁带离线图灵机的同时资源有界复杂性类，如时空有界类，记为NTISP1(T, S)，逆空间有界类，记为NRESP1(R, S)，时间反转有界类，记为NTIRE1(T, R)。由图可知，NRESP1(R(n)， S(n))包含NTISP1(S(n)， R(n) log n)，并包含在NTISP1(R(n) S(n)n2 log n, R(n) log n)中，得到以下推论:(1)非确定性单工作带版本NC = ?SC问题，NTIRE1(poly, polylog) = NTISP1(poly, polylog)，和(2)一个反向空间权衡，NRESP1(polylog, poly) = NRESP1(poly, polylog)。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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