{"title":"用双向随机磁带发生器进行概率空间的多项式确定性空间模拟是不存在的","authors":"Marek Karpinski , Rutger Verbeek","doi":"10.1016/S0019-9958(85)80032-2","DOIUrl":null,"url":null,"abstract":"<div><p>We prove there is no polynomial deterministic space simulation for two-way random-tape probabilistic space (Pr<sub>2</sub>SPACE) (as defined in Borodin, A., Cook, S., and Pippenger, N. (1983) <em>Inform. Control</em> <strong>58</strong> 113–136) for all functions <em>f</em>: ℕ → ℕ and all <em>α</em> ∈ ℕ, Pr<sub>2</sub>SPACE(<em>f</em>(<em>n</em>))DSPACE(<em>f</em>(<em>n</em>)<sup><em>α</em></sup>). This is the answer to the problem formulated in op cit., whether the deterministic squared-space simulation (for recognizers and transducers) generalizes to the two-way random-tape machine model. We prove, in fact, a stronger result saying that even space-bounded Las Vegas two-way random-tape algorithms (yielding always the correct answer and terminating with probability 1) are exponentially more efficient than the deterministic ones.</p></div>","PeriodicalId":38164,"journal":{"name":"信息与控制","volume":"67 1","pages":"Pages 158-162"},"PeriodicalIF":0.0000,"publicationDate":"1985-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0019-9958(85)80032-2","citationCount":"9","resultStr":"{\"title\":\"There is no polynomial deterministic space simulation of probabilistic space with a two-way random-tape generator\",\"authors\":\"Marek Karpinski , Rutger Verbeek\",\"doi\":\"10.1016/S0019-9958(85)80032-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We prove there is no polynomial deterministic space simulation for two-way random-tape probabilistic space (Pr<sub>2</sub>SPACE) (as defined in Borodin, A., Cook, S., and Pippenger, N. (1983) <em>Inform. Control</em> <strong>58</strong> 113–136) for all functions <em>f</em>: ℕ → ℕ and all <em>α</em> ∈ ℕ, Pr<sub>2</sub>SPACE(<em>f</em>(<em>n</em>))DSPACE(<em>f</em>(<em>n</em>)<sup><em>α</em></sup>). This is the answer to the problem formulated in op cit., whether the deterministic squared-space simulation (for recognizers and transducers) generalizes to the two-way random-tape machine model. We prove, in fact, a stronger result saying that even space-bounded Las Vegas two-way random-tape algorithms (yielding always the correct answer and terminating with probability 1) are exponentially more efficient than the deterministic ones.</p></div>\",\"PeriodicalId\":38164,\"journal\":{\"name\":\"信息与控制\",\"volume\":\"67 1\",\"pages\":\"Pages 158-162\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1985-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S0019-9958(85)80032-2\",\"citationCount\":\"9\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"信息与控制\",\"FirstCategoryId\":\"1093\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0019995885800322\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"信息与控制","FirstCategoryId":"1093","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0019995885800322","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 9
摘要
我们证明双向随机磁带概率空间(Pr2SPACE)(如Borodin, A., Cook, S.和Pippenger, N. (1983) Inform中定义的)不存在多项式确定性空间模拟。对于所有函数f: _1→_1和所有α∈_1,Pr2SPACE(f(n))DSPACE(f(n)α)。这就是在op - cit中提出的问题的答案,即确定性的平方空间模拟(用于识别器和换能器)是否可以推广到双向随机磁带机模型。事实上,我们证明了一个更强的结果,即即使是有空间限制的拉斯维加斯双向随机磁带算法(总是产生正确答案并以概率1结束)也比确定性算法的效率要高得多。
There is no polynomial deterministic space simulation of probabilistic space with a two-way random-tape generator
We prove there is no polynomial deterministic space simulation for two-way random-tape probabilistic space (Pr2SPACE) (as defined in Borodin, A., Cook, S., and Pippenger, N. (1983) Inform. Control58 113–136) for all functions f: ℕ → ℕ and all α ∈ ℕ, Pr2SPACE(f(n))DSPACE(f(n)α). This is the answer to the problem formulated in op cit., whether the deterministic squared-space simulation (for recognizers and transducers) generalizes to the two-way random-tape machine model. We prove, in fact, a stronger result saying that even space-bounded Las Vegas two-way random-tape algorithms (yielding always the correct answer and terminating with probability 1) are exponentially more efficient than the deterministic ones.