2009 24th Annual IEEE Conference on Computational Complexity最新文献_第3页

A Multi-Round Communication Lower Bound for Gap Hamming and Some Consequences Gap Hamming的多轮通信下界及其若干结果

2009 24th Annual IEEE Conference on Computational Complexity Pub Date : 2009-02-13 DOI: 10.1109/CCC.2009.31

Joshua Brody, Amit Chakrabarti

{"title":"A Multi-Round Communication Lower Bound for Gap Hamming and Some Consequences","authors":"Joshua Brody, Amit Chakrabarti","doi":"10.1109/CCC.2009.31","DOIUrl":"https://doi.org/10.1109/CCC.2009.31","url":null,"abstract":"The Gap-Hamming-Distance problem arose in the context of proving space lower bounds for a number of key problems in the data stream model. In this problem, Alice and Bob have to decide whether the Hamming distance between their $n$-bit input strings is large (i.e., at least $n/2 + sqrt n$) or small (i.e., at most $n/2 - sqrt n$); they do not care if it is neither large nor small. This $Theta(sqrt n)$ gap in the problem specification is crucial for capturing the approximation allowed to a data stream algorithm. Thus far, for randomized communication, an $Omega(n)$ lower bound on this problem was known only in the one-way setting. We prove an $Omega(n)$ lower bound for randomized protocols that use any constant number of rounds. As a consequence we conclude, for instance, that $epsilon$-approximately counting the number of distinct elements in a data stream requires $Omega(1/epsilon^2)$ space, even with multiple (a constant number of) passes over the input stream. This extends earlier one-pass lower bounds, answering a long-standing open question. We obtain similar results for approximating the frequency moments and for approximating the empirical entropy of a data stream. In the process, we also obtain tight $n - Theta(sqrt{n}log n)$ lower and upper bounds on the one-way deterministic communication complexity of the problem. Finally, we give a simple combinatorial proof of an $Omega(n)$ lower bound on the one-way randomized communication complexity.","PeriodicalId":158572,"journal":{"name":"2009 24th Annual IEEE Conference on Computational Complexity","volume":"168 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127198841","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: 38

A Superpolynomial Lower Bound on the Size of Uniform Non-constant-depth Threshold Circuits for the Permanent 永久性均匀非定深阈值电路尺寸的一个超多项式下界

2009 24th Annual IEEE Conference on Computational Complexity Pub Date : 2009-02-11 DOI: 10.1109/CCC.2009.19

P. Koiran, Sylvain Perifel

引用次数: 13

An Almost Optimal Rank Bound for Depth-3 Identities 深度-3恒等式的几乎最优秩界

2009 24th Annual IEEE Conference on Computational Complexity Pub Date : 2008-11-19 DOI: 10.1137/090770679

Nitin Saxena, C. Seshadhri

引用次数: 53

Oracularization and Two-Prover One-Round Interactive Proofs against Nonlocal Strategies 非局部策略的oracle化和双证明者一轮交互证明

2009 24th Annual IEEE Conference on Computational Complexity Pub Date : 2008-10-03 DOI: 10.1109/CCC.2009.22

Tsuyoshi Ito, Hirotada Kobayashi, Keiji Matsumoto

{"title":"Oracularization and Two-Prover One-Round Interactive Proofs against Nonlocal Strategies","authors":"Tsuyoshi Ito, Hirotada Kobayashi, Keiji Matsumoto","doi":"10.1109/CCC.2009.22","DOIUrl":"https://doi.org/10.1109/CCC.2009.22","url":null,"abstract":"This paper presents three results on the power of two-prover one-round interactive proof systems based on oracularization under the existence of prior entanglement between dishonest provers. It is proved that the two-prover one-round interactive proof system for PSPACE by Cai, Condon, and Lipton [JCSS 48:183-193, 1994] still achieves exponentially small soundness error in the existence of prior entanglement between dishonest provers (and more strongly, even if dishonest provers are allowed to use arbitrary no-signaling strategies). It follows that, unless the polynomial-time hierarchy collapses to the second level, two-prover systems are still advantageous to single-prover systems even when only malicious provers can use quantum information. It is also shown that a \"dummy\" question may be helpful when constructing an entanglement-resistant multi-prover system via oracularization. This affirmatively settles a question posed by Kempe et al. [FOCS 2008, pp. 447-456] and every language in NEXP is proved to have a two-prover one-round interactive proof system even against entangled provers, albeit with exponentially small gap between completeness and soundness. In other words, it is NP-hard to approximate within an inverse-polynomial the value of a classical two-prover one-round game against entangled provers. Finally, both for the above proof system for NEXP and for the quantum two-prover one-round proof system for NEXP proposed by Kempe et al., it is proved that exponentially small completeness-soundness gaps are best achievable unless soundness analysis uses the structure of the underlying system with unentangled provers.","PeriodicalId":158572,"journal":{"name":"2009 24th Annual IEEE Conference on Computational Complexity","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115218388","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: 74

An Approximation Algorithm for Approximation Rank 一种近似秩的近似算法

2009 24th Annual IEEE Conference on Computational Complexity Pub Date : 2008-09-11 DOI: 10.1109/CCC.2009.25

Troy Lee, A. Shraibman

引用次数: 30

Parallel Approximation of Non-interactive Zero-sum Quantum Games 非交互零和量子博弈的并行逼近

2009 24th Annual IEEE Conference on Computational Complexity Pub Date : 2008-08-20 DOI: 10.1109/CCC.2009.26

Rahul Jain, John Watrous

引用次数: 40

A New Characterization of ACC^0 and Probabilistic CC^0 ACC^0和概率CC^0的新表征

2009 24th Annual IEEE Conference on Computational Complexity Pub Date : 1900-01-01 DOI: 10.1109/CCC.2009.15

Kristoffer Arnsfelt Hansen, M. Koucký

{"title":"A New Characterization of ACC^0 and Probabilistic CC^0","authors":"Kristoffer Arnsfelt Hansen, M. Koucký","doi":"10.1109/CCC.2009.15","DOIUrl":"https://doi.org/10.1109/CCC.2009.15","url":null,"abstract":"Barrington, Straubing and Therien (1990) conjectured that the Boolean AND function can not be computed by polynomial size constant depth circuits built from modular counting gates, i.e., by CC^0 circuits. In this work we show that the AND function can be computed by uniform probabilistic CC^0 circuits that use only O(log n) random bits. This may be viewed as evidence contrary to the conjecture. As a consequence of our construction we get that all of ACC^0 can be computed by probabilistic CC^0 circuits that use only O(log n) random bits. Thus, if one were able to derandomize such circuits, we would obtain a collapse of circuit classes giving ACC^0=CC^0. We present a derandomization of probabilistic CC^0 circuits using AND and OR gates to obtain ACC^0 = AND o OR o CC^0 = OR o AND o CC^0. AND and OR gates of sublinear fan-in suffice. Both these results hold for uniform as well as non-uniform circuit classes. For non-uniform circuits we obtain the stronger conclusion that ACC^0 = rand-ACC^0 = rand-CC^0 = rand(log n)-CC^0, i.e., probabilistic ACC^0 circuits can be simulated by probabilistic CC^0 circuits using only O(log n) random bits. As an application of our results we obtain a characterization of ACC^0 by constant width planar nondeterministic branching programs, improving a previous characterization for the quasipolynomial size setting.","PeriodicalId":158572,"journal":{"name":"2009 24th Annual IEEE Conference on Computational Complexity","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122246457","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: 14