Filters








111 Hits in 5.9 sec

Hadamard tensors and lower bounds on multiparty communication complexity

Jeff Ford, Anna Gál
2012 Computational Complexity  
We also exhibit constructions of Hadamard tensors, giving Ω(n/2 k ) lower bounds on multiparty communication complexity for a new class of explicitly defined Boolean functions.  ...  Separating ACC 0 from other complexity classes (e.g. NP) is a major open problem, and a sufficiently large multiparty communication complexity lower bound would resolve it.  ...  Proving similar upper bounds on the weight of explicitly defined tensors would yield lower bounds of the form Ω(n) on multiparty communication complexity, for any number of players.  ... 
doi:10.1007/s00037-012-0052-6 fatcat:er2wewhfmvgujlngi62vsav4ka

Hadamard Tensors and Lower Bounds on Multiparty Communication Complexity [chapter]

Jeff Ford, Anna Gál
2005 Lecture Notes in Computer Science  
We also exhibit constructions of Hadamard tensors, giving Ω(n/2 k ) lower bounds on multiparty communication complexity for a new class of explicitly defined Boolean functions.  ...  Separating ACC 0 from other complexity classes (e.g. NP) is a major open problem, and a sufficiently large multiparty communication complexity lower bound would resolve it.  ...  Proving similar upper bounds on the weight of explicitly defined tensors would yield lower bounds of the form Ω(n) on multiparty communication complexity, for any number of players.  ... 
doi:10.1007/11523468_94 fatcat:sjdrhja7cjeedafbsacfmzvuiu

Disjointness is Hard in the Multiparty Number-on-the-Forehead Model

Troy Lee, Adi Shraibman
2009 Computational Complexity  
For k = 2 tight bounds are known of Θ(n) for randomized communication complexity [KS87] and Θ( √ n) for quantum communication complexity [Raz03, AA05].  ...  Our results give a separation between nondeterministic and randomized multiparty number-on-the-forehead communication complexity for up to k = log log n−O(log log log n) many players.  ...  Spalek, Emanuele Viola, Fengming Wang, Avi Wigderson, and Ronald de Wolf.  ... 
doi:10.1007/s00037-009-0276-2 fatcat:ovvpwvx6s5g2fncwviztxd5ice

Disjointness Is Hard in the Multi-party Number-on-the-Forehead Model

Troy Lee, Adi Shraibman
2008 2008 23rd Annual IEEE Conference on Computational Complexity  
For k = 2 tight bounds are known of Θ(n) for randomized communication complexity [KS87] and Θ( √ n) for quantum communication complexity [Raz03, AA05].  ...  Our results give a separation between nondeterministic and randomized multiparty number-on-the-forehead communication complexity for up to k = log log n−O(log log log n) many players.  ...  Spalek, Emanuele Viola, Fengming Wang, Avi Wigderson, and Ronald de Wolf.  ... 
doi:10.1109/ccc.2008.29 dblp:conf/coco/LeeS08 fatcat:b66xomhev5adddw6ry6qjny6xa

Disjointness is hard in the multi-party number on the forehead model [article]

Troy Lee, Adi Shraibman
2009 arXiv   pre-print
Our results give a separation between nondeterministic and randomized multiparty number-on-the-forehead communication complexity for up to k=log log n - O(log log log n) many players.  ...  Also by a reduction of Beame, Pitassi, and Segerlind, these results imply subexponential lower bounds on the size of proofs needed to refute certain unsatisfiable CNFs in a broad class of proof systems  ...  Spalek, Emanuele Viola, Fengming Wang, Avi Wigderson, and Ronald de Wolf.  ... 
arXiv:0712.4279v2 fatcat:52kcpauesrc77jxduzp46vnx44

Lower Bounds on Quantum Multiparty Communication Complexity

Troy Lee, Gideon Schechtman, Adi Shraibman
2009 2009 24th Annual IEEE Conference on Computational Complexity  
We show that essentially all lower bounds known on randomized complexity in this model also hold for quantum communication.  ...  Here we show how the γ2 norm can be also extended to lower bound quantum multiparty complexity.  ...  complexity; very large as our lower bound on multiparty quantum communication complexity loses a multiplicative factor of 1/k, which the classical bound does not.  ... 
doi:10.1109/ccc.2009.24 dblp:conf/coco/LeeSS09 fatcat:xdkmaizlw5am5bajl657r3lsdq

Partition Arguments in Multiparty Communication Complexity [article]

Jan Draisma and Eyal Kushilevitz and Enav Weinreb
2009 arXiv   pre-print
We conclude with two results on the multiparty "fooling set technique", another method for obtaining communication complexity lower bounds.  ...  The main lower bound technique for the communication complexity of such problems is that of partition arguments: partition the k players into two disjoint sets of players and find a lower bound for the  ...  We wish to thank Ronald de Wolf for useful discussions and, in particular, for referring us to [5] .  ... 
arXiv:0909.5684v1 fatcat:d2l6qqvghva3laylfahsc2gtki

Partition Arguments in Multiparty Communication Complexity [chapter]

Jan Draisma, Eyal Kushilevitz, Enav Weinreb
2009 Lecture Notes in Computer Science  
We conclude with two results on the multiparty "fooling set technique", another method for obtaining communication complexity lower bounds.  ...  The main lower bound technique for the communication complexity of such problems is that of partition arguments: partition the k players into two disjoint sets of players and find a lower bound for the  ...  The first author was partially supported by MSRI (Berkeley) and by NWO mathematics cluster DIAMANT.  ... 
doi:10.1007/978-3-642-02927-1_33 fatcat:i2igbsjri5bpvk2ihf6xjysiwe

Partition arguments in multiparty communication complexity

Jan Draisma, Eyal Kushilevitz, Enav Weinreb
2011 Theoretical Computer Science  
We conclude with two results on the multiparty "fooling set technique", another method for obtaining communication complexity lower bounds.  ...  The main lower bound technique for the communication complexity of such problems is that of partition arguments: partition the k players into two disjoint sets of players and find a lower bound for the  ...  The first author was partially supported by MSRI (Berkeley) and by NWO mathematics cluster DIAMANT.  ... 
doi:10.1016/j.tcs.2010.01.018 fatcat:ctic7v4wznco7hxtfi6mxmozw4

Exponential Quantum-Classical Gaps in Multiparty Nondeterministic Communication Complexity [article]

Xiaoming Sun, Marcos Villagra
2013 arXiv   pre-print
The proof of it involves an application of the pattern tensor method and a new lower bound for polynomial threshold degree.  ...  This also implies an exponential separation with respect to classical multiparty nondeterministic communication complexity.  ...  This gives a gap between all modes of communication mentioned above and NQP-communication complexity which is upper-bounded by the nondeterministic tensor-rank of the communication tensor in the Number-On-Forehead  ... 
arXiv:1308.2450v2 fatcat:rcgdspii6jcwbkisrkisem7ini

Communication Lower Bounds Using Dual Polynomials [article]

Alexander A. Sherstov
2008 arXiv   pre-print
lower bounds for DISJOINTNESS; (4) David and Pitassi's separation of NP and BPP in multiparty communication complexity for k=(1-eps)log n players.  ...  into upper bounds on the discrepancy of a related function; (2) Two different methods for proving lower bounds on bounded-error communication based on the approximate degree: Sherstov's pattern matrix  ...  Acknowledgments I would like to thank Anil Ada, Boaz Barak, Arkadev Chattopadhyay, Adam Klivans, Troy Lee, Yaoyun Shi, and Ronald de Wolf for their helpful feedback on a preliminary version of this survey  ... 
arXiv:0805.2135v1 fatcat:jsftr65cw5hqtbt2s67zvy2gve

A Separation of NP and coNP in Multiparty Communication Complexity [article]

Dmitry Gavinsky, Alexander A. Sherstov
2010 arXiv   pre-print
We prove that NP differs from coNP and coNP is not a subset of MA in the number-on-forehead model of multiparty communication complexity for up to k = (1-ϵ)log(n) players, where ϵ>0 is any constant.  ...  Specifically, we construct a function F with co-nondeterministic complexity O(log(n)) and Merlin-Arthur complexity n^Ω(1). The problem was open for k > 2.  ...  Previous Techniques Perhaps the best-known method for communication lower bounds, both in the number-on-forehead multiparty model and various two-party models, is the discrepancy method [KN] .  ... 
arXiv:1004.0817v1 fatcat:6zgtshhi7nauxoh7ghiyixx7f4

Applications of Monotone Rank to Complexity Theory [article]

Yang D. Li
2011 arXiv   pre-print
communication complexity and the logarithm of the rank of the communication tensor.  ...  In this paper, we follow Raz's work and show that monotone rank, the monotone variant of tensor rank and matrix rank, has applications in algebraic complexity, quantum computing and communication complexity  ...  complexity to the multiparty case, and prove that for super-polynomial parties, there is a super-polynomial separation between the deterministic communication complexity and the logarithm of the rank  ... 
arXiv:1102.2932v2 fatcat:qnochfkjnzcejazehjabn6ceh4

Distributed Quantum Computing [chapter]

Harry Buhrman, Hein Röhrig
2003 Lecture Notes in Computer Science  
In this paper we give a short introduction to quantum computing and survey the results in the area of distributed quantum computing and its applications to physics.  ...  problem is whether the communication complexity is also a lower bound for the log-rank.  ...  In this section we examine the converse and turn our attention to lower bounds for quantum communication complexity.  ... 
doi:10.1007/978-3-540-45138-9_1 fatcat:63gfw422i5bfrimhgqxxa6d6qy

Local hidden variable values without optimization procedures [article]

Dardo Goyeneche, Wojciech Bruzda, Ondřej Turek, Daniel Alsina, Karol Życzkowski
2022 arXiv   pre-print
In this work, we establish a relation between the LHV value of bipartite Bell inequalities and the mathematical notion of excess of a matrix.  ...  [27, [33] [34] [35] [36] [37] [38] , complex Hadamard matrices [39] , Hadamard tensors [40] and orthogonal designs [41] .  ...  Interestingly, maximal excess for tensors is connected with the socalled discrepancy of multivariable functions, associated with certain multiparty communication problems, see [40] and references therein  ... 
arXiv:2004.00695v3 fatcat:rhhqiaefync5zeqxmwz3birwyq
« Previous Showing results 1 — 15 out of 111 results