Super-linear gate and super-quadratic wire lower bounds for depth-two and depth-three threshold circuits
暂无分享,去创建一个
[1] J. Littlewood,et al. On the Number of Real Roots of a Random Algebraic Equation , 1938 .
[2] J. Littlewood,et al. On the number of real roots of a random algebraic equation. II , 1939 .
[3] P. Erdös. On a lemma of Littlewood and Offord , 1945 .
[4] C. K. Chow,et al. On the characterization of threshold functions , 1961, SWCT.
[5] Marvin Minsky,et al. Perceptrons: An Introduction to Computational Geometry , 1969 .
[6] Robert O. Winder,et al. Threshold logic , 1971, IEEE Spectrum.
[7] References , 1971 .
[8] Saburo Muroga,et al. Threshold logic and its applications , 1971 .
[9] Andrew Chi-Chih Yao,et al. Separating the Polynomial-Time Hierarchy by Oracles (Preliminary Version) , 1985, FOCS.
[10] Avi Wigderson,et al. Deterministic simulation of probabilistic constant depth circuits , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).
[11] Avi Wigderson,et al. Deterministic Simulation of Probabilistic Constant Depth Circuits (Preliminary Version) , 1985, FOCS 1985.
[12] G. Palm. Warren McCulloch and Walter Pitts: A Logical Calculus of the Ideas Immanent in Nervous Activity , 1986 .
[13] Johan Håstad,et al. Almost optimal lower bounds for small depth circuits , 1986, STOC '86.
[14] Pavel Pudlák,et al. Threshold circuits of bounded depth , 1987, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).
[15] Moni Naor,et al. Decision trees and downward closures , 1988, [1988] Proceedings. Structure in Complexity Theory Third Annual Conference.
[16] W S McCulloch,et al. A logical calculus of the ideas immanent in nervous activity , 1990, The Philosophy of Artificial Intelligence.
[17] Noga Alon,et al. Simple construction of almost k-wise independent random variables , 1990, Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science.
[18] György Turán,et al. On Linear Decision Trees Computing Boolean Functions , 1991, ICALP.
[19] Uri Zwick,et al. Shrinkage of de Morgan formulae under restriction , 1991, [1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science.
[20] Noga Alon,et al. Simple Construction of Almost k-wise Independent Random Variables , 1992, Random Struct. Algorithms.
[21] Alexander A. Razborov,et al. Majority gates vs. general weighted threshold gates , 1992, [1992] Proceedings of the Seventh Annual Structure in Complexity Theory Conference.
[22] N. Nisan. The communication complexity of threshold gates , 1993 .
[23] György Turán,et al. A Liniear lower bound for the size of threshold circuits , 1993, Bull. EATCS.
[24] Michael E. Saks,et al. Approximating Threshold Circuits by Rational Functions , 1994, Inf. Comput..
[25] K. Siu,et al. Theoretical Advances in Neural Computation and Learning , 1994, Springer US.
[26] Alon Orlitsky,et al. Lower bounds on threshold and related circuits via communication complexity , 1994, IEEE Trans. Inf. Theory.
[27] Alon Orlitsky,et al. Neural Models and Spectral Methods , 1994 .
[28] Michael E. Saks,et al. Size-depth trade-offs for threshold circuits , 1993, SIAM J. Comput..
[29] Johan Hå stad. The Shrinkage Exponent of de Morgan Formulas is 2 , 1998 .
[30] J. Håstad. The Shrinkage Exponent of de Morgan Formulas is 2 , 1998, SIAM J. Comput..
[31] Satyanarayana V. Lokam,et al. Relations Between Communication Complexity, Linear Arrangements, and Computational Complexity , 2001, FSTTCS.
[32] David Thomas,et al. The Art in Computer Programming , 2001 .
[33] Akira Maruoka,et al. On the Complexity of Depth-2 Circuits with Threshold Gates , 2005, MFCS.
[34] Michael Sipser,et al. Parity, circuits, and the polynomial-time hierarchy , 1981, 22nd Annual Symposium on Foundations of Computer Science (sfcs 1981).
[35] Eric Allender,et al. Amplifying Lower Bounds by Means of Self-Reducibility , 2008, 2008 23rd Annual IEEE Conference on Computational Complexity.
[36] Benjamin Rossman,et al. On the constant-depth complexity of k-clique , 2008, STOC.
[37] Ryan O'Donnell,et al. The chow parameters problem , 2008, SIAM J. Comput..
[38] Kristoffer Arnsfelt Hansen,et al. Exact Threshold Circuits , 2010, 2010 IEEE 25th Annual Conference on Computational Complexity.
[39] Rahul Santhanam,et al. Fighting Perebor: New and Improved Algorithms for Formula and QBF Satisfiability , 2010, 2010 IEEE 51st Annual Symposium on Foundations of Computer Science.
[40] Donald E. Knuth,et al. The Art of Computer Programming: Combinatorial Algorithms, Part 1 , 2011 .
[41] Johan Håstad,et al. On the Correlation of Parity and Small-Depth Circuits , 2014, SIAM J. Comput..
[42] Kazuhisa Seto,et al. A satisfiability algorithm and average-case hardness for formulas over the full binary basis , 2012, computational complexity.
[43] Russell Impagliazzo,et al. Pseudorandomness from Shrinkage , 2012, 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science.
[44] Ran Raz,et al. Improved Average-Case Lower Bounds for DeMorgan Formula Size , 2013, 2013 IEEE 54th Annual Symposium on Foundations of Computer Science.
[45] Russell Impagliazzo,et al. A Satisfiability Algorithm for Sparse Depth Two Threshold Circuits , 2012, 2013 IEEE 54th Annual Symposium on Foundations of Computer Science.
[46] Kristoffer Arnsfelt Hansen,et al. Polynomial threshold functions and Boolean threshold circuits , 2013, Inf. Comput..
[47] Ran Raz,et al. Average-case lower bounds for formula size , 2013, STOC '13.
[48] David Zuckerman,et al. Mining Circuit Lower Bound Proofs for Meta-Algorithms , 2014, computational complexity.
[49] Ryan Williams,et al. New algorithms and lower bounds for circuits with linear threshold gates , 2014, STOC.
[50] Rocco A. Servedio,et al. An Average-Case Depth Hierarchy Theorem for Boolean Circuits , 2015, 2015 IEEE 56th Annual Symposium on Foundations of Computer Science.
[51] Rahul Santhanam,et al. Average-Case Lower Bounds and Satisfiability Algorithms for Small Threshold Circuits , 2016, CCC.
[52] Huacheng Yu,et al. More Applications of the Polynomial Method to Algorithm Design , 2015, SODA.
[53] Valentine Kabanets,et al. An Improved Deterministic #SAT Algorithm for Small de Morgan Formulas , 2014, Algorithmica.
[54] Rahul Santhanam,et al. Improved Algorithms for Sparse MAX-SAT and MAX-k-CSP , 2015, SAT.
[55] Richard Ryan Williams. New Algorithms and Lower Bounds for Circuits With Linear Threshold Gates , 2018, Theory Comput..