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Randomized Complexity Lower Bound for Arrangements and Polyhedra

1999
*
Discrete & Computational Geometry
*

The

doi:10.1007/pl00009425
fatcat:bptptvesw5f27kp62ds3lltp2e
*complexity**lower**bound*(log N) for*randomized*computation trees is proved for recognizing an arrangement or a polyhedron with N faces. ... This provides in particular, the*randomized**lower**bound*(n log n) for the DISTINCTNESS problem and generalizes 11] where the*randomized**lower**bound*(n 2 ) was ascertained for the KNAPSACK problem. ... Relying on this*lower**bound*on the multiplicative*complexity*, the proof of the*complexity**lower**bound*(log N) for RCT recognizing an arrangement or a polyhedron with N faces (see the theorem in section ...##
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A lower bound for the discrepancy of a random point set

2014
*
Journal of Complexity
*

Consequently, the expected star discrepancy of a

doi:10.1016/j.jco.2013.06.001
fatcat:4bn4yx4w4bccdmfuhooc6skdnm
*random*point set is of order √(s/N). ... We show that there is a constant K > 0 such that for all N, s ∈, s < N, the point set consisting of N points chosen uniformly at*random*in the s-dimensional unit cube [0,1]^s with probability at least ... Surprisingly, not even a*lower**bound*for the discrepancy of a*random*point set is known. ...##
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Lower bounds for randomized and quantum query complexity using Kolmogorov arguments
[article]

2003
*
arXiv
*
pre-print

We prove a very general

arXiv:quant-ph/0311189v1
fatcat:24r2oyo6kbbwpc4fpgwlkz4fcq
*lower**bound*technique for quantum and*randomized*query*complexity*, that is easy to prove as well as to apply. ... As an immediate consequence of our main theorem, adversary methods can only prove*lower**bounds*for boolean functions f in O((√(n C_0(f)),√(n C_1(f)))), where C_0, C_1 is the certificate*complexity*, and ... Introduction Overview In this paper, we study*lower**bounds*for*randomized*and quantum query*complexity*. ...##
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Lower Bounds on the Randomized Communication Complexity of Read-Once Functions

2010
*
Computational Complexity
*

We prove

doi:10.1007/s00037-010-0292-2
fatcat:hiy5kdsiibbldhp73h3owfzgu4
*lower**bounds*on the*randomized*two-party communication*complexity*of functions that arise from read-once boolean formulae. ... In this paper we use information theory methods to prove*lower**bounds*that hold for any read-once formula. ... We also thank the anonymous referees of the 24th IEEE Conference on Computational*Complexity*and the Computational*Complexity*journal for their corrections and useful suggestions. ...##
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Improved lower bounds on the randomized complexity of graph properties

2007
*
Random structures & algorithms (Print)
*

We prove a

doi:10.1002/rsa.20164
fatcat:pmyrmhdenzhxhaqetkcnjxrkte
*lower**bound*of (n 4/3 log 1/3 n) on the*randomized*decision tree*complexity*of any nontrivial monotone n-vertex graph property, and of any nontrivial monotone bipartite graph property with bipartitions ... This improves the previous best*bound*of (n 4/3 ) due to Hajnal [Haj91]. ... Returning to*randomized**complexity*(the focus of this paper), the first nonlinear*lower**bound*on C R (P), for general P ∈ P n , was an (n log 1/12 n)*bound*proven by Yao [Yao87] . ...##
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Lower bounds for the complexity of linear functionals in the randomized setting

2011
*
Journal of Complexity
*

We also present

doi:10.1016/j.jco.2010.08.002
fatcat:uaoinntnvjchro2r6wmnb2vq6a
*lower**bounds*for reproducing kernels that are not decomposable but have a decomposable part. However, in this case it is not clear if the*lower**bounds*are sharp. ... Hinrichs [3] recently studied multivariate integration defined over reproducing kernel Hilbert spaces in the*randomized*setting and for the normalized error criterion. ... We must admit that after we completed the paper [5] on*lower**bounds*in the worst case setting, we started to work on*lower**bounds*in the*randomized*setting around the year 2002. ...##
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Improved Lower Bounds on the Randomized Complexity of Graph Properties
[chapter]

2001
*
Lecture Notes in Computer Science
*

We prove a

doi:10.1007/3-540-48224-5_24
fatcat:mlml6mbvdfcvrd3h5d5a6z7qaq
*lower**bound*of (n 4/3 log 1/3 n) on the*randomized*decision tree*complexity*of any nontrivial monotone n-vertex graph property, and of any nontrivial monotone bipartite graph property with bipartitions ... This improves the previous best*bound*of (n 4/3 ) due to Hajnal [Haj91]. ... Returning to*randomized**complexity*(the focus of this paper), the first nonlinear*lower**bound*on C R (P), for general P ∈ P n , was an (n log 1/12 n)*bound*proven by Yao [Yao87] . ...##
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Lower bounds in communication complexity based on factorization norms

2009
*
Random structures & algorithms (Print)
*

We introduce a new method to derive

doi:10.1002/rsa.20232
fatcat:ec546rrdsneyhmt4j3gij7d6xi
*lower**bounds*on*randomized*and quantum communication*complexity*. Our method is based on factorization norms, a notion from Banach Space theory. ... Among our new results we extend some known*lower**bounds*to the realm of quantum communication*complexity*with entanglement. ... Introduction We study*lower**bounds*for*randomized*and quantum communication*complexity*. ...##
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A lower bound for randomized algebraic decision trees

1996
*
Computational Complexity
*

As an application, among other things, we derive, for the first time, an f~(n 2)

doi:10.1007/bf01270387
fatcat:5mckzdtgl5futpdwltgc6qcuo4
*randomized**lower**bound*for the Knapsack Problem, and an ft(n logn)*randomized**lower**bound*for the Element Distinctness Problem ... We prove the first nontrivial (and superlinear)*lower**bounds*on the depth of*randomized*algebraic decision trees (with two-sided error) for problems being finite unions of hyperplanes and intersections ... []*Lower**bound*on the*complexity*of deterministic decision trees For d -DT T' which recognizes either an arrangement S or a polyhedron S +, we can give the similar*complexity**lower**bound*~(log N) ...##
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An Improved Lower Bound for the Randomized Decision Tree Complexity of Recursive Majority,
[chapter]

2013
*
Lecture Notes in Computer Science
*

In 2011, Magniez, Nayak, Santha, and Xiao, improved the

doi:10.1007/978-3-642-39206-1_59
fatcat:sjvfccrhjncx5ogtvetuzuv75a
*lower**bound*to Ω (5/2) d and the upper*bound*to O(2.64946 d ). ... We prove that the*randomized*decision tree*complexity*of the recursive majority-of-three is Ω(2.55 d ), where d is the depth of the recursion. ... We prove a*lower**bound*on the*randomized*decision tree*complexity*of the recursive majority-ofthree function. ...##
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Nondeterministic Circuit Lower Bounds from Mildly De-randomizing Arthur-Merlin Games

2012
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2012 IEEE 27th Conference on Computational Complexity
*

Our equivalence result represents a full analogue of a similar result by Impagliazzo et al. in the deterministic setting:

doi:10.1109/ccc.2012.32
dblp:conf/coco/AydinliogluM12
fatcat:b4dgncxwyrhgrmziowvmkssihm
*Randomized*polynomial-time decision procedures can be simulated in NSUBEXP (the ... INTRODUCTION The power of*randomness*constitutes a central topic in*complexity*theory. ... As the circuit*lower**bounds*seem plausible, even at the high end, the hardness versus*randomness*tradeoffs have fueled the conjecture that prBPP can be fully derandomized to P, and prAM to NP. ...##
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Lower Bounds for Randomized and Quantum Query Complexity Using Kolmogorov Arguments

2008
*
SIAM journal on computing (Print)
*

We prove a very general

doi:10.1137/050639090
fatcat:p64in7p24vcwthswopb25hhj5u
*lower**bound*technique for quantum and*randomized*query*complexity*, that is easy to prove as well as to apply. ... We also derive a general form of the ad hoc weighted method used by Høyer, Neerbek and Shi to give a quantum*lower**bound*on ordered search and sorting. ... Introduction Overview In this paper, we study*lower**bounds*for*randomized*and quantum query*complexity*. ...##
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Stronger Lower Bounds and Randomness-Hardness Trade-Offs Using Associated Algebraic Complexity Classes

2012
*
Symposium on Theoretical Aspects of Computer Science
*

We prove the following

doi:10.4230/lipics.stacs.2012.519
dblp:conf/stacs/JansenS12
fatcat:qe34yv6bfnekzl2jzrmc7eg5p4
*lower**bound*and*randomness*-to-hardness results: 1. ... The third item improves a*lower**bound*due to Santhanam [11] . ... However, it doesn't tell us whether these will be Boolean*lower**bounds*or arithmetic*lower**bounds*. ...##
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Lower bounds on random-self-reducibility

*
Proceedings Fifth Annual Structure in Complexity Theory Conference
*

Such functions are fundamental in many areas of theoretical computer science, including

doi:10.1109/sct.1990.113959
dblp:conf/coco/FeigenbaumKN90
fatcat:vwerkcayyvec5g5npfebebkg2a
*lower**bounds*, pseudorandom number-generators, interactive proof systems, zeroknowledge, instance-hiding, program-checking ... For example, we show unconditionally that*random*boolean functions do not have*random*-selfreductions, even of a quite general nature. ...*random*-self-reducibility would nd more applications in*complexity*theory and in practice. ...##
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Lower bounds for randomized and quantum query complexity using Kolmogorov arguments

*
Proceedings. 19th IEEE Annual Conference on Computational Complexity, 2004.
*

We prove a very general

doi:10.1109/ccc.2004.1313852
dblp:conf/coco/LaplanteM04
fatcat:7mlg5ylqubgilhtnofmo46mhu4
*lower**bound*technique for quantum and*randomized*query*complexity*, that is easy to prove as well as to apply. ... We also derive a general form of the ad hoc weighted method used by Høyer, Neerbek and Shi to give a quantum*lower**bound*on ordered search and sorting. ... Introduction Overview In this paper, we study*lower**bounds*for*randomized*and quantum query*complexity*. ...
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