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On Medium-Uniformity and Circuit Lower Bounds

Rahul Santhanam, Ryan Williams
2013 2013 IEEE Conference on Computational Complexity  
Eliminating Non-Uniformity and (Non-Uniform) Circuit Lower Bounds.  ...  Using a new kind of indirect diagonalization argument, we prove several new unconditional lower bounds against medium uniform circuit classes, including: • For all k, P is not contained in P-uniform SIZE  ...  Eliminating Non-Uniformity and (Non-Uniform) Circuit Lower Bounds.  ... 
doi:10.1109/ccc.2013.40 dblp:conf/coco/SanthanamW13 fatcat:mm4ls445rjd37mkuqv5sg2lqiy

On Uniformity and Circuit Lower Bounds

Rahul Santhanam, Ryan Williams
2014 Computational Complexity  
Eliminating non-uniformity and (non-uniform) circuit lower bounds.  ...  Using a new kind of indirect diagonalization argument, we prove several new unconditional lower bounds against medium-uniform circuit classes, including: • For all k, P is not contained in P-uniform SIZE  ...  R.S. was supported in part by the 2013 ERC Consolidator Grant ALUnif: "Algorithms and Lower Bounds: A Unified Approach."  ... 
doi:10.1007/s00037-014-0087-y fatcat:4fy5xs7jrfbtzm37apd7wq2qza

Page 9241 of Mathematical Reviews Vol. , Issue 2001M [page]

2001 Mathematical Reviews  
the first nontrivial time-space lower bounds for SAT on non-uniform machines.  ...  Klaus Meer (DK-SU-CS; Odense) 2001m:68053 68Q15 68Q17 Tourlakis, Iannis (3-TRNT-C; Toronto, ON) Time-space lower bounds for SAT on uniform and non-uniform machines.  ... 

Page 5097 of Mathematical Reviews Vol. , Issue 2000g [page]

2000 Mathematical Reviews  
We derive one result via new lower bounds on the degrees of poly- nomials asserted to exist by Hilbert’s Nullstellensatz over finite fields.” © 1998 Academic Press {For the entire collection see MR 99e  ...  monotone lower bounds without sunflowers.  ... 

Efficient Learning Algorithms Yield Circuit Lower Bounds [chapter]

Lance Fortnow, Adam R. Klivans
2006 Lecture Notes in Computer Science  
Our approach uses the framework of the breakthrough result due to Kabanets and Impagliazzo showing that derandomizing BPP yields non-trivial circuit lower bounds.  ...  We describe a new approach for understanding the difficulty of designing efficient learning algorithms.  ...  and non-uniform circuit classes.  ... 
doi:10.1007/11776420_27 fatcat:2doc46s7mba7bk4dzhjxaznsti

Efficient learning algorithms yield circuit lower bounds

Lance Fortnow, Adam R. Klivans
2009 Journal of computer and system sciences (Print)  
Our approach uses the framework of the breakthrough result due to Kabanets and Impagliazzo showing that derandomizing BPP yields non-trivial circuit lower bounds.  ...  We describe a new approach for understanding the difficulty of designing efficient learning algorithms.  ...  and non-uniform circuit classes.  ... 
doi:10.1016/j.jcss.2008.07.006 fatcat:tb56jbg74zazfcb2vfviik4wgy

Page 5476 of Mathematical Reviews Vol. , Issue 2003g [page]

2003 Mathematical Reviews  
The class of black-box functions considered for proving the lower bound has measure | with respect to U.  ...  via (non-uniform) depth-three AC’-circuits.  ... 

On TC0 Lower Bounds for the Permanent [chapter]

Jeff Kinne
2012 Lecture Notes in Computer Science  
An ongoing line of research has shown super-polynomial lower bounds for slightly-non-uniform small-depth threshold and arithmetic circuits [All99, KP09, JS11, JS12].  ...  In this paper we consider the problem of proving lower bounds for the permanent.  ...  We thank Matt in particular for observations that refined the statement of Theorem 2. We also thank the reviewers for comments and suggestions that improved the exposition of the paper.  ... 
doi:10.1007/978-3-642-32241-9_36 fatcat:mw2gulyr7fbp3pvodrtik7e7sa

Amplifying Circuit Lower Bounds against Polynomial Time with Applications

Richard J. Lipton, Ryan Williams
2012 2012 IEEE 27th Conference on Computational Complexity  
Moreover, the resulting circuits require onlyÕ(n ε ) bits of non-uniformity to construct.  ...  This implies unconditional polynomial-time uniform circuit lower bounds for solving QBF. We also prove that QBF does not have n c -time uniform NC circuits, for all c < 2.  ...  Acknowledgements We are grateful to the referees for helpful comments which improved the presentation.  ... 
doi:10.1109/ccc.2012.44 dblp:conf/coco/LiptonW12 fatcat:6wgwlinj7ber5fsqnw3b2l2vdu

Amplifying circuit lower bounds against polynomial time, with applications

Richard J. Lipton, Ryan Williams
2013 Computational Complexity  
Moreover, the resulting circuits require onlyÕ(n ε ) bits of non-uniformity to construct.  ...  This implies unconditional polynomial-time uniform circuit lower bounds for solving QBF. We also prove that QBF does not have n c -time uniform NC circuits, for all c < 2.  ...  Acknowledgements We are grateful to the referees for helpful comments which improved the presentation.  ... 
doi:10.1007/s00037-013-0069-5 fatcat:ngha5frjwfecfla2kyq26pwtia

Lower bounds for wrap-around L2-discrepancy and constructions of symmetrical uniform designs

Kai-Tai Fang, Yu Tang, Jianxing Yin
2005 Journal of Complexity  
In this paper, explicit lower bounds of the wrap-around L 2 -discrepancy of U-type designs are obtained. Sufficient conditions for U-type designs to achieve their lower bounds are given.  ...  We also propose an efficient balance-pursuit heuristic, by which we find many new uniform designs, especially with high levels.  ...  Acknowledgments We thank both referees for their suggestions, comments and remarks which greatly help us to improve the presentation of this paper.  ... 
doi:10.1016/j.jco.2005.01.003 fatcat:ea2uuxuakzhufajif3gpbjw564

3-Message Zero Knowledge Against Human Ignorance [chapter]

Nir Bitansky, Zvika Brakerski, Yael Kalai, Omer Paneth, Vinod Vaikuntanathan
2016 Lecture Notes in Computer Science  
Resolving the precise round complexity of zero-knowledge has been an outstanding open problem for far too long.  ...  In this work, we present a three-message zero-knowledge argument system with soundness against uniform polynomial-time cheating provers.  ...  We thank Ran Canetti, Shai Halevi and Hugo Krawczyk for helpful comments and for pointing out the connection to [Rog06] .  ... 
doi:10.1007/978-3-662-53641-4_3 fatcat:7s3dzvhiubgjpaosjwkhsrp4sa

Bounded-width polynomial-size branching programs recognize exactly those languages in NC1

David A. Barrington
1989 Journal of computer and system sciences (Print)  
As any bounded-width polynomial-size branching program can be simulated by an NC 1 circuit, we have that the class of languages recognized by such programs is exactly non-uniform NC 1 .  ...  We also extend the method of proof to investigate the complexity of the word problem for a fixed permutation group.  ...  I would like to thank him for all his help and also thank Ravi Boppana, Johan Hastad, Philip Klein, Tom Leighton, and Leslie Valiant for various helpful discussions.  ... 
doi:10.1016/0022-0000(89)90037-8 fatcat:uorbc2viwngnhms7kzcerquium

Bounded-width polynomial-size branching programs recognize exactly those languages in NC1

D A Barrington
1986 Proceedings of the eighteenth annual ACM symposium on Theory of computing - STOC '86  
As any bounded-width polynomial-size branching program can be simulated by an NC 1 circuit, we have that the class of languages recognized by such programs is exactly non-uniform NC 1 .  ...  We also extend the method of proof to investigate the complexity of the word problem for a fixed permutation group.  ...  I would like to thank him for all his help and also thank Ravi Boppana, Johan Hastad, Philip Klein, Tom Leighton, and Leslie Valiant for various helpful discussions.  ... 
doi:10.1145/12130.12131 dblp:conf/stoc/Barrington86 fatcat:h5wnfosbozhxpiv5iwz6vg7zn4

NEXP Does Not Have Non-uniform Quasipolynomial-Size ACC Circuits of o(loglogn) Depth [chapter]

Fengming Wang
2011 Lecture Notes in Computer Science  
We show that there exists a language in non-deterministic exponential time which can not be computed by any non-uniform family of ACC m circuits of quasipolynomial size and o(log log n) depth, where m  ...  Acknowledgement We thank Eric Allender, Luke Friedman and Ryan Williams for helpful discussions.  ...  We are especially grateful to Eric Allender for carefully reading earlier drafts and providing many useful comments.  ... 
doi:10.1007/978-3-642-20877-5_17 fatcat:lxkowswvgvc2bbzj6dgnf232qu
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