Twenty-Second Annual IEEE Conference on Computational Complexity (CCC'07)最新文献_第2页

Lower Bounds for Multi-Player Pointer Jumping 多玩家指针跳跃的下限

Twenty-Second Annual IEEE Conference on Computational Complexity (CCC'07) Pub Date : 2007-06-13 DOI: 10.1109/CCC.2007.14

Amit Chakrabarti

{"title":"Lower Bounds for Multi-Player Pointer Jumping","authors":"Amit Chakrabarti","doi":"10.1109/CCC.2007.14","DOIUrl":"https://doi.org/10.1109/CCC.2007.14","url":null,"abstract":"We consider the k-layer pointer jumping problem in the one-way multi-party number-on-the-forehead communication model. Sufficiently strong lower bounds for the problem would have major consequences in circuit complexity. We take an information complexity approach to this problem and obtain three lower bounds that improve upon earlier work. For myopic protocols (where players may see only one layer ahead but arbitrarily far behind), we greatly improve a lower bound due to Gronemeier (2006). Our new lower bound is Omega(n/k), where n is the number of vertices per layer. For conservative protocols (where players may see arbitrarily far ahead but not behind, instead seeing only the vertex reached by following the pointers up to their layer), we extend an Omega(n/k2) lower bound due to Damm, Jukna and Sgall (1998) so that it applies for all k. The above two bounds apply even to the Boolean version of pointer jumping. Our third lower bound is for the non-Boolean case and for k les log* n. We obtain an Omega(n log(k-1) n) bound for myopic protocols. Damm et al. had obtained a similar bound for deterministic conservative protocols. All our lower bounds apply directly to randomised protocols.","PeriodicalId":175854,"journal":{"name":"Twenty-Second Annual IEEE Conference on Computational Complexity (CCC'07)","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127953579","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: 33

Norms, XOR Lemmas, and Lower Bounds for GF(2) Polynomials and Multiparty Protocols GF(2)多项式和多方协议的范数、异或引理和下界

Twenty-Second Annual IEEE Conference on Computational Complexity (CCC'07) Pub Date : 2007-06-13 DOI: 10.1109/CCC.2007.15

Emanuele Viola, A. Wigderson

{"title":"Norms, XOR Lemmas, and Lower Bounds for GF(2) Polynomials and Multiparty Protocols","authors":"Emanuele Viola, A. Wigderson","doi":"10.1109/CCC.2007.15","DOIUrl":"https://doi.org/10.1109/CCC.2007.15","url":null,"abstract":"This paper presents a unified and simple treatment of basic questions concerning two computational models: multiparty communication complexity and GF(2) polynomials. The key is the use of (known) norms on Boolean functions, which capture their approximability in each of these models. The main contributions are new XOR lemmas. We show that if a Boolean function has correlation at most epsi les 1/2 with any of these models, then the correlation of the parity of its values on m independent instances drops exponentially with m. More specifically: For GF(2) polynomials of degree d, the correlation drops to exp (-m/4d). No XOR lemma was known even for d = 2. For c-bit k-party protocols, the correlation drops to 2c ldrepsim/2 k . No XOR lemma was known for k ges 3 parties. Another contribution in this paper is a general derivation of direct product lemmas from XOR lemmas. In particular, assuming that f has correlation at most epsi les 1/2 with any of the above models, we obtain the following bounds on the probability of computing m independent instances of f correctly: For GF(2) polynomials of degree d we again obtain a bound of exp(-m/4d). For c-bit k-party protocols we obtain a bound of 2-Omega(m) in the special case when epsi les exp (-c ldr 2k). In this range of epsi, our bound improves on a direct product lemma for two-parties by Parnafes, Raz, and Wigderson (STOC '97). We also use the norms to give improved (or just simplified) lower bounds in these models. In particular we give a new proof that the Modm function on n bits, for odd m, has correlation at most exp(-n/4d) with degree-d GF(2) polynomials.","PeriodicalId":175854,"journal":{"name":"Twenty-Second Annual IEEE Conference on Computational Complexity (CCC'07)","volume":"112 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124121421","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: 57

On Derandomizing Probabilistic Sublinear-Time Algorithms 非随机化概率次线性时间算法

Twenty-Second Annual IEEE Conference on Computational Complexity (CCC'07) Pub Date : 2007-06-13 DOI: 10.1109/CCC.2007.19

Marius Zimand

引用次数: 6

Directed Planar Reachability is in Unambiguous Log-Space 无二义对数空间中的有向平面可达性

Twenty-Second Annual IEEE Conference on Computational Complexity (CCC'07) Pub Date : 2007-06-13 DOI: 10.1145/1490270.1490274

Chris Bourke, Raghunath Tewari, N. V. Vinodchandran

引用次数: 76

On Parameterized Path and Chordless Path Problems 关于参数化路径和无弦路径问题

Twenty-Second Annual IEEE Conference on Computational Complexity (CCC'07) Pub Date : 2007-06-13 DOI: 10.1109/CCC.2007.21

Yijia Chen, J. Flum

引用次数: 43

Quantum t-designs: t-wise Independence in the Quantum World 量子t型设计:量子世界中的t型独立

Twenty-Second Annual IEEE Conference on Computational Complexity (CCC'07) Pub Date : 2007-01-17 DOI: 10.1109/CCC.2007.26

A. Ambainis, J. Emerson

引用次数: 164

Quantum versus Classical Proofs and Advice 量子与经典的证明和建议

Twenty-Second Annual IEEE Conference on Computational Complexity (CCC'07) Pub Date : 2006-04-09 DOI: 10.4086/toc.2007.v003a007

S. Aaronson, G. Kuperberg

{"title":"Quantum versus Classical Proofs and Advice","authors":"S. Aaronson, G. Kuperberg","doi":"10.4086/toc.2007.v003a007","DOIUrl":"https://doi.org/10.4086/toc.2007.v003a007","url":null,"abstract":"This paper studies whether quantum proofs are more powerful than classical proofs, or in complexity terms, whether QMA = QCMA. We prove three results about this question. First, we give a \"quantum oracle separation\" between QMA and QCM A. More concretely, we show that any quantum algorithm needs Omega (radic2n-m+1) queries to find an n-qubit \"marked state\" Psi rang, even if given an m-bit classical description of Psi rang together with a quantum black box that recognizes Psi rang. Second, we give an explicit QCMA protocol that nearly achieves this lower bound. Third, we show that, in the one previously-known case where quantum proofs seemed to provide an exponential advantage, classical proofs are basically just as powerful. In particular, Wa- trous gave a QM IK protocol for verifying non-membership infinite groups. Under plausible group-theoretic assumptions, we give a QCMA protocol for the same problem. Even with no assumptions, our protocol makes only poly-nomially many queries to the group oracle. We end with some conjectures about quantum versus classical oracles, and about the possibility of a classical oracle separation between QMA and QCMA.","PeriodicalId":175854,"journal":{"name":"Twenty-Second Annual IEEE Conference on Computational Complexity (CCC'07)","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130279093","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: 86

Ronald V. Book Prize for Best Student Paper Award 罗纳德·v·图书奖最佳学生论文奖

Twenty-Second Annual IEEE Conference on Computational Complexity (CCC'07) Pub Date : 1900-01-01 DOI: 10.1109/ccc.2007.29

引用次数: 0