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A linear lower bound on the unbounded error probabilistic communication complexity

Jürgen Forster
2002 Journal of computer and system sciences (Print)  
the spectral norm of the matrix M: This implies a general lower bound on the complexity of unbounded error probabilistic communication protocols.  ...  As a simple consequence, we obtain the first linear lower bound on the complexity of unbounded error probabilistic communication protocols for the functions defined by Hadamard matrices.  ...  Acknowledgments The author wants to thank Hans Ulrich Simon for a lot of helpful comments and for telling him about a nice idea how random projection and results from communication complexity theory can  ... 
doi:10.1016/s0022-0000(02)00019-3 fatcat:bsogu6iu4vb7birmwryzvhjqnq

A linear lower bound on the unbounded error probabilistic communication complexity

J. Forster
Proceedings 16th Annual IEEE Conference on Computational Complexity  
We prove a general lower bound on the complexity of unbounded error probabilistic communication protocols. This result improves on a lower bound for bounded error protocols from Krause.  ...  As a simple consequence we get the, to our knowledge, rst linear lower bound on the complexity of unbounded error probabilistic communication protocols for the functions de ned by Hadamard matrices.  ...  prove upper bounds on margins of arrangements of half spaces.  ... 
doi:10.1109/ccc.2001.933877 dblp:conf/coco/Forster01 fatcat:47tegreyzjdl7lagqyn4l6sn3q

Probabilistic communication complexity

Ramamohan Paturi, Janos Simon
1986 Journal of computer and system sciences (Print)  
Further, we apply the logarithmic lower bound on communication complexity to obtain an Q(n log n) bound on the time of l-tape unbounded error probabilistic Turing machines.  ...  Communication is a bottleneck in many distributed computations. In VLSI, communication constraints dictate lower bounds on the performance of chips.  ...  In particular, the idea of using rank 1 matrices is due to Prasanna Kumar and Schnitger, who obtained an (essentially equivalent) lower bound.  ... 
doi:10.1016/0022-0000(86)90046-2 fatcat:6qtle3lbafaatpnonrk2xqqtdq

Geometric arguments yield better bounds for threshold circuits and distributed computing

Matthias Krause
1996 Theoretical Computer Science  
We consider the following norm llfll for Boolean functions f : (0, I}" x (0, I}" + (0, I}: llfll = max{lM(f*)ul,  ...  These are to prove superpolynomial lower bounds on the number of edges of depth three threshold circuits and superlogarithmic lower bounds on the length of unbounded error probabilistic communication protocols  ...  Previous lower bound arguments for probabilistic communication complexity and depth two threshold circuits are based on the following fact.  ... 
doi:10.1016/0304-3975(95)00005-4 fatcat:y3avu7lvfzh37abcgiqlqxcfhy

On the power of circuits with gates of low L1 norms

Vince Grolmusz
1997 Theoretical Computer Science  
Then we present several applications of this theorem for circuit lower bounds (both for bounded-and unbounded depth), and a decision-tree lower bound.  ...  IP function and the DISJ function with exponential Lt norms have linear (both deterministic and probabilistic) communication complexity [9,20,30].  ...  Supported in part by the European Communities contract number ERBCIPACT930 113.  ... 
doi:10.1016/s0304-3975(96)00290-3 fatcat:evlgn22tdbbk5iq6p56kv3uyc4

Page 2643 of Mathematical Reviews Vol. , Issue 88e [page]

1988 Mathematical Reviews  
The techniques are also used to obtain an Q(n log n) lower bound on the time of 1-tape unbounded error probabilistic Turing machines.  ...  The purpose of this paper is to provide some insight into communi- cation complexity in the unbounded error probabilistic model.  ... 

Probabilistic Rank and Matrix Rigidity [article]

Josh Alman, Ryan Williams
2017 arXiv   pre-print
We demonstrate several connections with matrix rigidity, communication complexity, and circuit lower bounds, including: The Walsh-Hadamard Transform is Not Very Rigid.  ...  We consider a notion of probabilistic rank and probabilistic sign-rank of a matrix, which measures the extent to which a matrix can be probabilistically represented by low-rank matrices.  ...  s conjectures and results on non-rigidity at Banff (BIRS) in August 2016.  ... 
arXiv:1611.05558v2 fatcat:lqij2wpjzrduxoa3g5iswj6q2a

Lower Bounds for Quantum Communication Complexity

Hartmut Klauck
2007 SIAM journal on computing (Print)  
We prove new lower bounds on quantum bounded error communication complexity. Our methods are based on the Fourier transform of the considered functions.  ...  This follows from a characterization of the discrepancy bound in terms of (quantum or classical probabilistic) protocols with weakly unbounded error.  ...  Acknowledgement The author wishes to thank Ronald de Wolf for pointing out [27] and for lots of valuable discussions.  ... 
doi:10.1137/s0097539702405620 fatcat:mir6s4heincbfldkrqfcvgqqoa

Page 1397 of Mathematical Reviews Vol. , Issue 2004b [page]

2004 Mathematical Reviews  
Huimin Xie (PRC-SOO; Suzhou) 2004b:68062 68Q17 15A60 94A05 Forster, Jiirgen (D-BCHMM-MI; Bochum) A linear lower bound on the unbounded error probabilistic communication complexity.  ...  A consequence of this result is that the unbounded error prob- abilistic communication complexity of the functions defined by Hadamard matrices is linear.  ... 

Page 6549 of Mathematical Reviews Vol. , Issue 2000i [page]

2000 Mathematical Reviews  
We give a number of upper and lower bounds for problems stemming from query-processing, invoking in the process tools from the area of communication complexity.”  ...  We discuss this for both bounded-error and unbounded-error probabilistic classes. In addition to these tree model variations, we show invariance in def- initional representations of the class PP.  ... 

On Multiparty Communication with Large versus Unbounded Error

Alexander A. Sherstov
2018 Theory of Computing  
The unbounded-error communication complexity of a Boolean function F is the limit of the ε-error randomized complexity of F as ε → 1/2.  ...  In more detail, we construct a k-party communication problem F : ({0, 1} n ) k → {0, 1} that has complexity O(log n) with unbounded error and Ω( √ n/4 k ) with weakly unbounded error, reproducing the bounds  ...  Acknowledgments The author is thankful to Arkadev Chattopadhyay and Nikhil Mande for a stimulating discussion and helpful feedback on an earlier version of this manuscript.  ... 
doi:10.4086/toc.2018.v014a022 dblp:journals/toc/Sherstov18 fatcat:22iarbucqfbxvh7laz2zlov2sm

Lower bounds for quantum communication complexity [article]

Hartmut Klauck
2002 arXiv   pre-print
We then prove the first large lower bounds on the bounded error quantum communication complexity of functions, for which a polynomial quantum speedup is possible.  ...  We prove new lower bounds for bounded error quantum communication complexity. Our methods are based on the Fourier transform of the considered functions.  ...  The author wishes to thank Ronald de Wolf for bringing [34] to his attention and for lots of valuable discussions, and Andris Ambainis for pointing out a mistake in an earlier version of the paper.  ... 
arXiv:quant-ph/0106160v3 fatcat:sc36lnmjareavfzcu75bk6mlfq

Algebra in Computational Complexity (Dagstuhl Seminar 14391)

Manindra Agrawal, Valentine Kabanets, Thomas Thierauf, Christopher Umans, Marc Herbstritt
2015 Dagstuhl Reports  
NP and circuit lower bounds, the effort to resolve the complexity of matrix multiplication, and a framework for constructing locally testable codes.  ...  There have been significant recent advances in algebraic circuit lower bounds, and the so-called "chasm at depth 4" suggests that the restricted models now being considered are not so far from ones that  ...  Rahul showed a lower bound on the communication complexity of the Mod q -function, for any prime q = p.  ... 
doi:10.4230/dagrep.4.9.85 dblp:journals/dagstuhl-reports/AgrawalKTU14 fatcat:iailudx2rrhaxenbi3d7ou73ly

Dual polynomials and communication complexity of XOR functions [article]

Arkadev Chattopadhyay, Nikhil S. Mande
2017 arXiv   pre-print
Using this duality, we develop polynomial based techniques for understanding the bounded error (BPP) and the weakly-unbounded error (PP) communication complexities of XOR functions.  ...  Zhang and Shi assert that for symmetric functions f : {0, 1}^n →{-1, 1}, the weakly unbounded-error complexity of f ∘XOR is essentially characterized by the number of points i in the set {0,1, ...  ...  We thank Justin Thaler for pointers regarding the connection between margin and threshold weight, and bringing the recent paper of Hatami and Qian [18] to our notice.  ... 
arXiv:1704.02537v1 fatcat:zcaw7jsb6rch7fsv3pkkjavz34

One-way communication complexity and the Neciporuk lower bound on formula size [article]

Hartmut Klauck
2004 arXiv   pre-print
In all cases we can use results about one-way communication complexity to prove lower bounds on formula size. In the latter two cases we newly develop the employed communication complexity bounds.  ...  In this paper the Neciporuk method for proving lower bounds on the size of Boolean formulae is reformulated in terms of one-way communication complexity.  ...  The author wishes to thank Gregor Gramlich for a talk on the Nečiporuk method, which inspired this research, and Georg Schnitger for stimulating discussions.  ... 
arXiv:cs/0111062v2 fatcat:ycnaen7igje2pkw75v6syfjukq
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