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Towards proving strong direct product theorems

Ronen Shaltiel
2003 Computational Complexity  
Still, in order to 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.  ... 
doi:10.1007/s00037-003-0175-x fatcat:fyjjyay4ozhvpiuqdgexisoo5m

Towards proving strong direct product theorems

R. Shaltiel
Proceedings 16th Annual IEEE Conference on Computational Complexity  
Still, in order to 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.  ... 
doi:10.1109/ccc.2001.933878 dblp:conf/coco/Shaltiel01 fatcat:vmonxmpdafbypbw76x3jyic32a

NZ-flows in strong products of graphs

Wilfried Imrich, Iztok Peterin, Simon Špacapan, Cun-Quan Zhang
2009 Journal of Graph Theory  
We 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).  ... 
doi:10.1002/jgt.20455 fatcat:5ozke4u52jdbnpqroa67bpettq

George Sudarshan, No-Go theorems and the exclusion principle

M Y Han
2009 Journal of Physics, Conference Series  
Georges insight into the spinstatistics relationship was indispensable in the birth of the new theory of the 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.  ... 
doi:10.1088/1742-6596/196/1/012008 fatcat:njdfmqtnmjfofi36xshp4e4ayu

Guest Editorial for Information Complexity and Applications

Mark Braverman, David P. Woodruff
2016 Algorithmica  
In "A 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  ... 
doi:10.1007/s00453-016-0180-5 fatcat:j7bwxoqchneibjmuh3oemixulm

Special Issue on User Interfaces in Theorem Proving: Preface

David Aspinall, Christoph Lüth
2007 Journal of automated reasoning  
Yet there is universal recognition that interfaces must improve if 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.  ... 
doi:10.1007/s10817-007-9075-0 fatcat:ikxjp56qozhmbhqthymb7ntr7a

Hardness Amplification of Optimization Problems

Elazar Goldenberg, Karthik C. S., Michael Wagner
2020 Innovations in Theoretical Computer Science  
In this paper, we 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.  ... 
doi:10.4230/lipics.itcs.2020.1 dblp:conf/innovations/GoldenbergS20 fatcat:nqnlm74n65f7tm22q4hetqiiv4

Oriented colouring of some graph products

N.R. Aravind, N. Narayanan, C.R. Subramanian
2011 Discussiones Mathematicae Graph Theory  
We obtain some improved upper and lower bounds on the oriented chromatic number for different classes of 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.  ... 
doi:10.7151/dmgt.1572 fatcat:bbaczd4zwjcb3kynxfux363yxe

On the spanning trees of the hypercube and other products of graphs [article]

Olivier Bernardi
2012 arXiv   pre-print
The second proof uses some "killing involutions" in order to identify the factors in the 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.  ... 
arXiv:1207.0896v3 fatcat:wkec2ftvmfdy5oigsj2vhb7k3e

Strong preinjective partitions and representation type of Artinian rings

Birge Zimmermann-Huisgen
1990 Proceedings of the American Mathematical Society  
., for every ring all of whose left modules are 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 .  ... 
doi:10.1090/s0002-9939-1990-1007520-3 fatcat:bakvsmwzezboncpm7267vyowiq

Strong Preinjective Partitions and Representation Type of Artinian Rings

Birge Zimmermann-Huisgen
1990 Proceedings of the American Mathematical Society  
., for every ring all of whose left modules are 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 .  ... 
doi:10.2307/2047989 fatcat:lupk5lbc3jcjjhnot2gme7zhly

Equilibrium Bias of Technology

Daron Acemoglu
2005 Social Science Research Network  
I 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.  ... 
doi:10.2139/ssrn.861424 fatcat:an2jyxgujba5pg7nwxlvukdstm

Equilibrium Bias of Technology

Daron Acemoglu
2007 Econometrica  
I 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.  ... 
doi:10.1111/j.1468-0262.2007.00797.x fatcat:z6ynp7s7lbdu3na3bmrdekjlcm

Additive combinatorics with a view towards computer science and cryptography: An exposition [article]

Khodakhast Bibak
2012 arXiv   pre-print
Erdős and Turán [111] proposed a very 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.  ... 
arXiv:1108.3790v9 fatcat:wl3rd7geqrh7fkvotruo6fkk3u

Towards understanding the Pierce–Birkhoff conjecture via MV-algebras

S. Lapenta, I. Leuştean
2015 Fuzzy sets and systems (Print)  
The proper quasi-variety generated by [0,1], with both 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  ... 
doi:10.1016/j.fss.2014.11.012 fatcat:blngfmis5rhvfnh3pj3j67gtdi
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