Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317)最新文献_第3页

Gaps in bounded query hierarchies 有界查询层次结构中的间隙

Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317) Pub Date : 1999-05-04 DOI: 10.1109/CCC.1999.766271

R. Beigel

{"title":"Gaps in bounded query hierarchies","authors":"R. Beigel","doi":"10.1109/CCC.1999.766271","DOIUrl":"https://doi.org/10.1109/CCC.1999.766271","url":null,"abstract":"Prior results show that most bounded query hierarchies cannot contain finite gaps. For example, it is known that P/sub (m+1)-tt//sup SAT/=P/sub m-tt//sup SAT//spl rArr/P/sub btt//sup SAT/=P/sub m-tt//sup SAT/ and for all sets A/spl middot/FP/sub (m=1)-tt//sup A/=FP/sub m-tt//sup A//spl rArr/FP/sub btt//sup A/=FP/sub m-tt//sup A//spl middot/P/sub (m+1)-T//sup A/=P/sub m-T//sup A/=P/sub bT//sup A//spl middot/FP/sub (m+1)-T//sup A/=FP/sub m-T//sup A//spl rArr/FP/sub bT//sup A/=FP/sub m-T//sup A/ where P/sub m-tt//sup A/ is the set of languages computable by polynomial-time Turing machines that make m nonadaptive queries to A; P/sub btt//sup A/=/spl cup//sub m/P/sub m-tt//sup A/, P/sub m-t//sup A/ and P/sub bT//sup A/ are the analogous adaptive queries classes; and FP/sub m-tt//sup A/, FP/sub btt//sup A/, FP/sub m-T//sup A/, and FP/sub bT//sup A/ in turn are the analogous function classes. It was widely expected that these general results would extend to the remaining case-languages computed with nonadaptive queries-yet results remained elusive. The best known was that P/sub 2m-tt//sup A/=P/sub m-tt//sup A//spl rArr/P/sub btt//sup A/=P/sub m-tt//sup A/. We disprove the conjecture, in fact, P/sub [4/3m]-tt//sup A/=P/sub m-tt//sup A/not/spl rArr/P/sub ([4/3m]+1)-tt/=P/sub [4/3m]-tt//sup A/. Thus there is a P/sub m-tt//sup A/ hierarchy that contains a finite gap. We also make progress on the 3-tt vs. 2-tt case: P/sub 3-tt//sup A/=P/sub 2-tt//sup A//spl rArr/P/sub btt//sup A//spl sube/P/sub 2-tt//sup A//poly.","PeriodicalId":432015,"journal":{"name":"Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129518949","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

Graph Ramsey theory and the polynomial hierarchy 图Ramsey理论与多项式层次

Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317) Pub Date : 1999-05-01 DOI: 10.1145/301250.301411

M. Schaefer

引用次数: 59

Linear gaps between degrees for the polynomial calculus modulo distinct primes 多项式演算对不同素数模的度之间的线性间隙

Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317) Pub Date : 1999-05-01 DOI: 10.1145/301250.301399

S. Buss, D. Grigoriev, R. Impagliazzo, T. Pitassi

{"title":"Linear gaps between degrees for the polynomial calculus modulo distinct primes","authors":"S. Buss, D. Grigoriev, R. Impagliazzo, T. Pitassi","doi":"10.1145/301250.301399","DOIUrl":"https://doi.org/10.1145/301250.301399","url":null,"abstract":"Two important algebraic proof systems are the Nullstellensatz system and the polynomial calculus (also called the Grobner system). The Nullstellensatz system is a propositional proof system based on Hilbert's Nullstellensatz, and the polynomial calculus (PC) is a proof system which allows derivations of polynomials, over some field. The complexity of a proof in these systems is measured in terms of the degree of the polynomials used in the proof. The mod p counting principle can be formulated as a set MOD/sub p//sup n/ of constant-degree polynomials expressing the negation of the counting principle. The Tseitin mod p principles, TS/sub n/(p), are translations of the MOD/sub p//sup n/ into the Fourier basis. The present paper gives linear lower bounds on the degree of polynomial calculus refutations of MOD/sub p//sup n/ over p fields of characteristic q /spl ne/ p and over rings Z/sub q/ with q,p relatively prime. These are the first linear lower bounds for the polynomial calculus. As it is well-known to be easy to give constant degree polynomial calculus (and even Nullstellensatz) refutations of the MOD/sub p//sup n/ polynomials over F/sub p/, our results imply that the MOD/sub p//sup n/ polynomials have a linear gap between proof complexity for the polynomial calculus over F/sub p/ and over F/sub q/. We also obtain a linear gap for the polynomial calculus over rings Z/sub p/ and Z/sub q/ where p, q do not have identical prime factors.","PeriodicalId":432015,"journal":{"name":"Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317)","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123081272","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 116

The communication complexity of pointer chasing. Applications of entropy and sampling 指针跟踪的通信复杂性。熵和抽样的应用

Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317) Pub Date : 1999-05-01 DOI: 10.1145/301250.301413

S. Ponzio, J. Radhakrishnan, Venkatesh Srinivasan

引用次数: 17

Quantum bounded query complexity 量子有界查询复杂度

Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317) Pub Date : 1999-03-09 DOI: 10.1109/CCC.1999.766273

H. Buhrman, W. V. Dam

引用次数: 12

The expected size of Heilbronn's triangles 海尔布隆三角形的预期大小

Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317) Pub Date : 1999-02-05 DOI: 10.1109/CCC.1999.766269

Tao Jiang, Ming Li, P. Vitányi

引用次数: 6

Quantum simulations of classical random walks and undirected graph connectivity 经典随机漫步和无向图连通性的量子模拟

Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317) Pub Date : 1998-12-10 DOI: 10.1109/CCC.1999.766275

John Watrous

{"title":"Quantum simulations of classical random walks and undirected graph connectivity","authors":"John Watrous","doi":"10.1109/CCC.1999.766275","DOIUrl":"https://doi.org/10.1109/CCC.1999.766275","url":null,"abstract":"There are a number of questions in quantum complexity that have been resolved in the time-bounded setting, but remain open in the space-bounded setting. For example, it is not currently known if space-bounded probabilistic computations can be simulated by space-bounded quantum machines without allowing measurements during the computation, while it is known that an analogous statement holds in the time-bounded case. A more general question asks if measurements during a quantum computation can allow for more space-efficient solutions to certain problems. In this paper we show that space-bounded quantum Turing machines can efficiently simulate a limited class of random processes-random walks on undirected graphs-without relying on measurements during the computation. By means of such simulations, it is demonstrated that the undirected graph connectivity problem for regular graphs can be solved by one-sided error quantum Turing machines that run in logspace and require a single measurement at the end of their computations. It follows that symmetric logspace is contained in the quantum analogue of randomized logspace, i.e., SL/spl sube/QR/sub H/L.","PeriodicalId":432015,"journal":{"name":"Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317)","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1998-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121768629","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 184

Pseudorandom generators without the XOR lemma 没有异或引理的伪随机生成器

Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317) Pub Date : 1900-01-01 DOI: 10.1109/CCC.1999.766253

M. Sudan, L. Trevisan, S. Vadhan

引用次数: 5