On the power of two-way random generators and the impossibility of deterministic poly-space simulation

Q4 Mathematics 信息与控制 Pub Date : 1986-10-01 DOI:10.1016/S0019-9958(86)80020-1
Marek Karpinski, Rutger Verbeek
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引用次数: 5

Abstract

Borodin, Cook, and Pippenger (Inform. and Control 58 (1983), 96–114) proved that both probabilistic acceptors and transducers working in space S(n) ⩾ log n can be simulated by deterministic machines in O(S(n)2) space. The definition of probabilistic computations uses one-way read-only random tape. Borodin et al. asked: “Is it possible to extend our simulation results to the case of a two-way read-only oracle head?” In the same vein Furst, Lipton, and Stockmeyer (Inform. and Control 64 (1985), 43–51) suggested that it could be a difference between two-way and one-way random tape: “…for space bounded probabilistic computations where the space bound is much less than the length of y, it could matter.” (y denoting the random tape inscription.) In this paper we give a full characterization of two-way random space classes that answers both questions. Karpinski and Verbeek (“There is no Polynomial Deterministic Space Simulation of Probabilistic Space with Two-way Random-Tape Generator,” Inform. and Control 67 (1985), 158–162) proved that there is no polynomial deterministic space simulation of two-way random space without giving any recursive upper bound. The results of this paper solved the open questions of Karpinski and Verbeek, 1985, Karpinski and Verbeek, 1985 and gave full characterization in sense of upper and lower deterministic space classes: they are proved precisely exponentially more powerful than the corresponding one-way classes.

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关于双向随机发生器的功率和确定性多空间仿真的不可能性
鲍罗丁、库克和皮彭格(通知)和Control 58(1983), 96-114)证明了在空间S(n)大于或等于log n的空间中工作的概率受体和传感器都可以通过O(S(n)2)空间中的确定性机器进行模拟。概率计算的定义使用单向只读随机磁带。Borodin等人问道:“是否有可能将我们的模拟结果扩展到双向只读oracle头的情况?”同样的道理,弗斯特、利普顿和斯托克梅耶(Inform。和Control 64(1985), 43-51)认为这可能是双向和单向随机磁带之间的区别:“……对于空间边界远小于y长度的空间边界概率计算,这可能很重要。(y表示随机的磁带铭文。)在本文中,我们给出了回答这两个问题的双向随机空间类的完整表征。Karpinski和Verbeek(“没有多项式确定性空间模拟的概率空间与双向随机磁带发生器,”Inform。和Control 67(1985), 158-162)证明了不给出任何递归上界就不存在双向随机空间的多项式确定性空间模拟。本文的结果解决了Karpinski和Verbeek, 1985, Karpinski和Verbeek, 1985的开放性问题,并给出了上下确定性空间类意义上的充分表征,证明了它们比相应的单向类具有精确的指数性。
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来源期刊
信息与控制
信息与控制 Mathematics-Control and Optimization
CiteScore
1.50
自引率
0.00%
发文量
4623
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