{"title":"单工作带不确定性图灵机的时间、空间和反转的同时关系","authors":"Etsuro Moriya, Shigeki Iwata, Takumi Kasai","doi":"10.1016/S0019-9958(86)80003-1","DOIUrl":null,"url":null,"abstract":"<div><p>Simultaneous resource bounded complexity classes for nondeterministic single worktape off-line Turing machines are considered such as time-space bounded classes, denoted by NTISP<sub>1</sub>(<em>T, S</em>), reversal-space bounded classes, denoted by NRESP<sub>1</sub>(<em>R, S</em>), and time-reversal bounded classes, denoted by NTIRE<sub>1</sub>(<em>T, R</em>). It is shown that NRESP<sub>1</sub>(<em>R</em>(<em>n</em>), <em>S</em>(<em>n</em>)) contains NTISP<sub>1</sub>(<em>S</em>(<em>n</em>), <em>R</em>(<em>n</em>)) and is contained in NTISP<sub>1</sub>(<em>R</em>(<em>n</em>) <em>S</em>(<em>n</em>)<em>n</em><sup>2</sup> log <em>n</em>, <em>R</em>(<em>n</em>) log <em>n</em>). The following corollaries follow: (1) the affirmative solution to the nondeterministic single worktape version of the <em>NC</em> = ? <em>SC</em> problem, NTIRE<sub>1</sub>(poly, polylog) = NTISP<sub>1</sub>(poly, polylog), and (2) a reversal-space trade-off, NRESP<sub>1</sub>(polylog, poly) = NRESP<sub>1</sub>(poly, polylog).</p></div>","PeriodicalId":38164,"journal":{"name":"信息与控制","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"1986-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0019-9958(86)80003-1","citationCount":"3","resultStr":"{\"title\":\"A note on some simultaneous relations among time, space, and reversal for single work tape nondeterministic turing machines\",\"authors\":\"Etsuro Moriya, Shigeki Iwata, Takumi Kasai\",\"doi\":\"10.1016/S0019-9958(86)80003-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Simultaneous resource bounded complexity classes for nondeterministic single worktape off-line Turing machines are considered such as time-space bounded classes, denoted by NTISP<sub>1</sub>(<em>T, S</em>), reversal-space bounded classes, denoted by NRESP<sub>1</sub>(<em>R, S</em>), and time-reversal bounded classes, denoted by NTIRE<sub>1</sub>(<em>T, R</em>). It is shown that NRESP<sub>1</sub>(<em>R</em>(<em>n</em>), <em>S</em>(<em>n</em>)) contains NTISP<sub>1</sub>(<em>S</em>(<em>n</em>), <em>R</em>(<em>n</em>)) and is contained in NTISP<sub>1</sub>(<em>R</em>(<em>n</em>) <em>S</em>(<em>n</em>)<em>n</em><sup>2</sup> log <em>n</em>, <em>R</em>(<em>n</em>) log <em>n</em>). The following corollaries follow: (1) the affirmative solution to the nondeterministic single worktape version of the <em>NC</em> = ? <em>SC</em> problem, NTIRE<sub>1</sub>(poly, polylog) = NTISP<sub>1</sub>(poly, polylog), and (2) a reversal-space trade-off, NRESP<sub>1</sub>(polylog, poly) = NRESP<sub>1</sub>(poly, polylog).</p></div>\",\"PeriodicalId\":38164,\"journal\":{\"name\":\"信息与控制\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1986-08-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S0019-9958(86)80003-1\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"信息与控制\",\"FirstCategoryId\":\"1093\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0019995886800031\",\"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/S0019995886800031","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
A note on some simultaneous relations among time, space, and reversal for single work tape nondeterministic turing machines
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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