Advice from Nonadaptive Queries to NP.pdfVIP

下载本文档

4
0
约2.92万字
约 14页
2017-04-11 发布于江苏
举报
版权申诉

Advice from Nonadaptive Queries to NP.pdf

1、有哪些信誉好的足球投注网站（book118）网站文档一经付费（服务费），不意味着购买了该文档的版权，仅供个人/单位学习、研究之用，不得用于商业用途，未经授权，严禁复制、发行、汇编、翻译或者网络传播等，侵权必究。。
2、本站所有内容均由合作方或网友上传，本站不对文档的完整性、权威性及其观点立场正确性做任何保证或承诺！文档内容仅供研究参考，付费前请自行鉴别。如您付费，意味着您自己接受本站规则且自行承担风险，本站不退款、不进行额外附加服务；查看《如何避免下载的几个坑》。如果您已付费下载过本站文档，您可以点击这里二次下载。
3、如文档侵犯商业秘密、侵犯著作权、侵犯人身权等，请点击“版权申诉”（推荐），也可以打举报电话：400-050-0827(电话支持时间：9:00-18:30)。
4、该文档为VIP文档，如果想要下载，成为VIP会员后，下载免费。
5、成为VIP后，下载本文档将扣除1次下载权益。下载后，不支持退款、换文档。如有疑问请联系我们。
6、成为VIP后，您将拥有八大权益，权益包括：VIP文档下载权益、阅读免打扰、文档格式转换、高级专利检索、专属身份标志、高级客服、多端互通、版权登记。
7、VIP文档为合作方或网友上传，每下载1次，网站将根据用户上传文档的质量评分、类型等，对文档贡献者给予高额补贴、流量扶持。如果你也想贡献VIP文档。上传文档

Advice from Nonadaptive Queries to NP

[CGH + 88] J. Cai, T. Gundermann, J. Hartmanis, L. Hemachandra, V. Sewelson, K. Wag- ner, and G. Wechsung. The boolean hierarchy I: Structural properties. SIAM Journal on Computing, 17(6):1232{1252, 1988. [HU79] J. Hopcroft and J. Ullman. Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, 1979. [KL82] R. Karp and R. Lipton. Turing machines that take advice. LEnseignement Mathematique, 28:191{209, 1982. [KSW87] J. Kobler, U. Schoning, and K. Wagner. The dierence and truth-table hierar- chies of NP. R.A.I.R.O. Informatique theorique et Applications, 21(4):419{435, 1987. [KT90] J. Kobler and T. Thierauf. Complexity classes with advice. In Proceedings of the 5th Structure in Complexity Theory Conference, pages 305{315. IEEE Computer Society Press, July 1990. To appear in SIAM Journal on Computing. [LLS75] R. Ladner, N. Lynch, and A. Selman. A comparison of polynomial time re- ducibilities. Theoretical Computer Science, 1(2):103{124, 1975. [Wec85] G. Wechsung. On the boolean closure of NP. In Proceedings of the 5th Confer- ence on Fundamentals of Computation Theory, pages 485{493. Springer-Verlag Lecture Notes in Computer Science #199 , 1985. (An unpublished precursor of this paper was coauthored by K. Wagner). 14 m, Mod NP[k] m functions are less powerful as advice to P evaluators than Mod NP[k] 2 functions, unless the boolean hierarchy collapses. Theorem 4.6 Let m 2 be odd and k 0. Then P==Mod NP[k] m = P==Mod NP[kbk=mc] 2 . Proof. Given Theorems 4.4 and 3.1, it suces to prove P==Mod NP[k] m P==# NP[kbk=mc] . Let L 2 P==Mod NP[k] m via a function f 2 Mod NP[k] m and a set B 2 P. Let f 1 ; . . . ; f k be FP functions such that for all x 2 , f(x) = SAT(f 1 (x)) + + SAT(f k (x)) (mod m). For i = 1; . . . ; k, we de ne the NP sets A i = f x j at least i of f 1 (x); . . . ; f k (x) are in SAT g and let h i be a many-one reduction from A i to SAT. Then f(x) = SAT(h 1 (x)) + + SAT(h k (x)) (mod m). Since the sets A i form