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Towards proving strong direct product theorems

2003
*
Computational Complexity
*

Still, in order to

doi:10.1007/s00037-003-0175-x
fatcat:fyjjyay4ozhvpiuqdgexisoo5m
*prove**theorems*with a*strong**direct**product*flavor we must change the formulation of the question and either strengthen the assumption or weaken the conclusion. ... for*strong**direct**product*assertions is false. ... In section 4 we*prove*a*strong**direct**product**theorem*for communication protocols via the discrepancy method. In section 5 we*prove*a*strong**direct**product**theorem*for fair decision trees. ...##
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Towards proving strong direct product theorems

*
Proceedings 16th Annual IEEE Conference on Computational Complexity
*

Still, in order to

doi:10.1109/ccc.2001.933878
dblp:conf/coco/Shaltiel01
fatcat:vmonxmpdafbypbw76x3jyic32a
*prove**theorems*with a*strong**direct**product*flavor we must change the formulation of the question and either strengthen the assumption or weaken the conclusion. ... for*strong**direct**product*assertions is false. ... In section 4 we*prove*a*strong**direct**product**theorem*for communication protocols via the discrepancy method. In section 5 we*prove*a*strong**direct**product**theorem*for fair decision trees. ...##
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NZ-flows in strong products of graphs

2009
*
Journal of Graph Theory
*

We

doi:10.1002/jgt.20455
fatcat:5ozke4u52jdbnpqroa67bpettq
*prove*that the*strong**product*G 1 G 2 of G 1 and G 2 is Z 3 -flow contractible if and only if G 1 G 2 is not T K 2 , where T is a tree (we call T K 2 a K 4 -tree). ... We will*prove*the above*theorems*in the following two sections. Z 3 -FLOW CONTRACTIBILITY OF*STRONG**PRODUCTS*In this section we*prove**Theorem*1. ... so that the edges are*directed**toward*the root). ...##
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George Sudarshan, No-Go theorems and the exclusion principle

2009
*
Journal of Physics, Conference Series
*

Georges insight into the spinstatistics relationship was indispensable in the birth of the new theory of the

doi:10.1088/1742-6596/196/1/012008
fatcat:njdfmqtnmjfofi36xshp4e4ayu
*strong*force. ... A series of proofs of no-go*theorems*by George, myself and others eventually led to the definitive proof by Lochlainn O'Raifeartaigh that came to be known as the ORaifeartaigh*theorem*. ... myself,*toward**proving*a series of such no-go*theorems*. By the way, the term no-go*theorems*was coined by Thomas Jordan, who will speak shortly in this session.M.E. Mayer, H.J. Schnitzer, E.C.G. ...##
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Guest Editorial for Information Complexity and Applications

2016
*
Algorithmica
*

In "A

doi:10.1007/s00453-016-0180-5
fatcat:j7bwxoqchneibjmuh3oemixulm
*Direct**Product**Theorem*for Two-Party Bounded-Round Public-Coin Communication Complexity" the authors*prove*the first*strong**direct**product**theorem*for any relation for two-party bounded round public-coin ... In "*Towards*a Reverse Newman's*Theorem*in Interactive Information Complexity" the authors*prove*that any bounded round protocol with private randomness can be converted into one using only public randomness ...##
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Special Issue on User Interfaces in Theorem Proving: Preface

2007
*
Journal of automated reasoning
*

Yet there is universal recognition that interfaces must improve if

doi:10.1007/s10817-007-9075-0
fatcat:ikxjp56qozhmbhqthymb7ntr7a
*theorem**proving*is to become more accessible and*productive*. ...*Theorem**proving*is coming of age. ... This special issue on User Interfaces in*Theorem**Proving*contains five papers reporting progress in this area, addressing the themes outlined above. ...##
###
Hardness Amplification of Optimization Problems

2020
*
Innovations in Theoretical Computer Science
*

In this paper, we

doi:10.4230/lipics.itcs.2020.1
dblp:conf/innovations/GoldenbergS20
fatcat:nqnlm74n65f7tm22q4hetqiiv4
*prove*a general hardness amplification scheme for optimization problems based on the technique of*direct**products*. ... Given a*direct**product*feasible optimization problem Π, our hardness amplification*theorem*may be informally stated as follows: If there is a distribution D over instances of Π of size n such that every ... Additionally, showing average-case hardness for functions is a stepping stone*towards**proving**strong*derandomization results and the construction of pseudorandom generators. ...##
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Oriented colouring of some graph products

2011
*
Discussiones Mathematicae Graph Theory
*

We obtain some improved upper and lower bounds on the oriented chromatic number for different classes of

doi:10.7151/dmgt.1572
fatcat:bbaczd4zwjcb3kynxfux363yxe
*products*of graphs. ... Conclusions We obtained bounds on oriented chromatic numbers for*products*of arbitrary graphs with paths. ... Oriented Colouring of Some Graph*Products*679 We also obtain the following for the*strong**product*of paths.*Theorem*3. ...##
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On the spanning trees of the hypercube and other products of graphs
[article]

2012
*
arXiv
*
pre-print

The second proof uses some "killing involutions" in order to identify the factors in the

arXiv:1207.0896v3
fatcat:wkec2ftvmfdy5oigsj2vhb7k3e
*product*formula. ... We give two combinatorial proofs of an elegant*product*formula for the number of spanning trees of the n-dimensional hypercube. ... The Cartesian*product*G × K 2 (top line) and the*strong**product*G ⊠ K 2 (bottom line). We start with a few definitions. ...##
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Strong preinjective partitions and representation type of Artinian rings

1990
*
Proceedings of the American Mathematical Society
*

., for every ring all of whose left modules are

doi:10.1090/s0002-9939-1990-1007520-3
fatcat:bakvsmwzezboncpm7267vyowiq
*direct*sums of finitely generated modules), the finitely generated left modules can be grouped to a unique "*strong*preinjective partition" while the finitely ... presented right modules possess a "*strong*preprojective partition"; these*strong*partitions are upgraded versions of the partitions introduced by Auslander and Smal0 for Artin algebras. ... and any index set I the*direct**product*C is isomorphic to a*direct*sum of copies of C . ...##
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Strong Preinjective Partitions and Representation Type of Artinian Rings

1990
*
Proceedings of the American Mathematical Society
*

., for every ring all of whose left modules are

doi:10.2307/2047989
fatcat:lupk5lbc3jcjjhnot2gme7zhly
*direct*sums of finitely generated modules), the finitely generated left modules can be grouped to a unique "*strong*preinjective partition" while the finitely ... presented right modules possess a "*strong*preprojective partition"; these*strong*partitions are upgraded versions of the partitions introduced by Auslander and Smal0 for Artin algebras. ... and any index set I the*direct**product*C is isomorphic to a*direct*sum of copies of C . ...##
###
Equilibrium Bias of Technology

2005
*
Social Science Research Network
*

I

doi:10.2139/ssrn.861424
fatcat:an2jyxgujba5pg7nwxlvukdstm
*prove*that under fairly mild assumptions, an increase in the supply of a factor always induces changes in technology that are absolutely biased*towards*that factor, and these results hold both for small ... This force can be*strong*enough to make the relative marginal*product*of a factor increasing in response to an increase in its supply, thus leading to an upward-sloping relative demand curve. ... This*theorem*will be*proved*by providing two examples with*strong*absolute equilibrium bias. ...##
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Equilibrium Bias of Technology

2007
*
Econometrica
*

I

doi:10.1111/j.1468-0262.2007.00797.x
fatcat:z6ynp7s7lbdu3na3bmrdekjlcm
*prove*that under fairly mild assumptions, an increase in the supply of a factor always induces changes in technology that are absolutely biased*towards*that factor, and these results hold both for small ... This force can be*strong*enough to make the relative marginal*product*of a factor increasing in response to an increase in its supply, thus leading to an upward-sloping relative demand curve. ... This*theorem*will be*proved*by providing two examples with*strong*absolute equilibrium bias. ...##
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Additive combinatorics with a view towards computer science and cryptography: An exposition
[article]

2012
*
arXiv
*
pre-print

Erdős and Turán [111] proposed a very

arXiv:1108.3790v9
fatcat:wl3rd7geqrh7fkvotruo6fkk3u
*strong*form of van der Waerden's*theorem*-the density version of van der Waerden's*theorem*. ... Much efforts have been made*towards*the value of ε. Elekes [107] observed that the sum-*product*problem has interesting connections to problems in incidence geometry. ...##
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Towards understanding the Pierce–Birkhoff conjecture via MV-algebras

2015
*
Fuzzy sets and systems (Print)
*

The proper quasi-variety generated by [0,1], with both

doi:10.1016/j.fss.2014.11.012
fatcat:blngfmis5rhvfnh3pj3j67gtdi
*products*interpreted as the real*product*, provides the desired framework: the normal form*theorem*of its corresponding logical system can be seen ... To do this we define the class of fMV-algebras, which are MV-algebras endowed with both an internal binary*product*and a scalar*product*with scalars from [0,1]. ... If A ∈ V, then U R (A) is a P M V + -algebras, and by [22, Corollary 4.4] it belongs to ISP ([0, 1]), therefore is A is a subalgebra of a*direct**product*of copies of [0, 1], and the*direct**product*is ...
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