A Case of Depth-3 Identity Testing, Sparse Factorization and Duality
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Nitin Saxena | Ramprasad Saptharishi | Chandan Saha | Nitin Saxena | Ramprasad Saptharishi | Chandan Saha
[1] Joos Heintz,et al. Testing polynomials which are easy to compute (Extended Abstract) , 1980, STOC '80.
[2] Nitin Saxena,et al. Progress on Polynomial Identity Testing , 2009, Bull. EATCS.
[3] J. Sylvester,et al. LX. On a remarkable discovery in the theory of canonical forms and of hyperdeterminants , 1851 .
[4] Nitin Saxena,et al. Progress on Polynomial Identity Testing - II , 2014, Electron. Colloquium Comput. Complex..
[5] Sanjeev Arora,et al. Probabilistic checking of proofs: a new characterization of NP , 1998, JACM.
[6] Ran Raz,et al. Lower Bounds and Separations for Constant Depth Multilinear Circuits , 2008, Computational Complexity Conference.
[7] Ran Raz. Multilinear-NC1 != Multilinear-NC2 , 2004, Electron. Colloquium Comput. Complex..
[8] Nitin Saxena,et al. Jacobian hits circuits: hitting-sets, lower bounds for depth-D occur-k formulas & depth-3 transcendence degree-k circuits , 2011, STOC '12.
[9] Manindra Agrawal,et al. Primality and identity testing via Chinese remaindering , 1999, 40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039).
[10] Richard J. Lipton,et al. A Probabilistic Remark on Algebraic Program Testing , 1978, Inf. Process. Lett..
[11] Richard Zippel,et al. Probabilistic algorithms for sparse polynomials , 1979, EUROSAM.
[12] Nitin Saxena,et al. Blackbox Identity Testing for Bounded Top-Fanin Depth-3 Circuits: The Field Doesn't Matter , 2012, SIAM J. Comput..
[13] Shubhangi Saraf,et al. Blackbox Polynomial Identity Testing for Depth 3 Circuits , 2009, 2009 50th Annual IEEE Symposium on Foundations of Computer Science.
[14] Carsten Lund,et al. Proof verification and the hardness of approximation problems , 1998, JACM.
[15] Manindra Agrawal. Determinant versus permanent , 2006 .
[16] Nitin Saxena,et al. An Almost Optimal Rank Bound for Depth-3 Identities , 2011, SIAM J. Comput..
[17] László Lovász,et al. On determinants, matchings, and random algorithms , 1979, FCT.
[18] Adi Shamir,et al. IP = PSPACE , 1992, JACM.
[19] Marek Karpinski,et al. On Zero-Testing and Interpolation of k-Sparse Multivariate Polynomials Over Finite Fields , 1991, Theor. Comput. Sci..
[20] Manindra Agrawal,et al. Classifying polynomials and identity testing , 2009 .
[21] Ilya Volkovich,et al. Derandomizing Polynomial Identity Testing for Multilinear Constant-Read Formulae , 2011, 2011 IEEE 26th Annual Conference on Computational Complexity.
[22] Manindra Agrawal,et al. PRIMES is in P , 2004 .
[23] Ketan Mulmuley,et al. On P vs. NP and geometric complexity theory: Dedicated to Sri Ramakrishna , 2011, JACM.
[24] Satyanarayana V. Lokam,et al. Reconstruction of depth-4 multilinear circuits with top fan-in 2 , 2012, STOC '12.
[25] Nitin Saxena,et al. Diagonal Circuit Identity Testing and Lower Bounds , 2008, ICALP.
[26] Nitin Saxena,et al. From Sylvester-Gallai Configurations to Rank Bounds: Improved Black-Box Identity Test for Depth-3 Circuits , 2010, FOCS.
[27] Manindra Agrawal,et al. Proving Lower Bounds Via Pseudo-random Generators , 2005, FSTTCS.
[28] Ran Raz,et al. Lower Bounds and Separations for Constant Depth Multilinear Circuits , 2008, 2008 23rd Annual IEEE Conference on Computational Complexity.
[29] Ran Raz,et al. A Lower Bound for the Size of Syntactically Multilinear Arithmetic Circuits , 2007, 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07).
[30] Erich Kaltofen,et al. Factoring Sparse Multivariate Polynomials , 1983, J. Comput. Syst. Sci..
[31] Waring's problem for commutative rings , 1987 .
[32] Russell Impagliazzo,et al. Derandomizing Polynomial Identity Tests Means Proving Circuit Lower Bounds , 2003, STOC '03.
[33] Pascal Koiran,et al. Shallow circuits with high-powered inputs , 2010, ICS.
[34] Ran Raz,et al. Deterministic polynomial identity testing in non-commutative models , 2004, Proceedings. 19th IEEE Annual Conference on Computational Complexity, 2004..
[35] Zhi-Zhong Chen,et al. Reducing Randomness via Irrational Numbers , 2000, SIAM J. Comput..
[36] Zeev Dvir,et al. Locally Decodable Codes with Two Queries and Polynomial Identity Testing for Depth 3 Circuits , 2007, SIAM J. Comput..
[37] Amir Yehudayoff,et al. Arithmetic Circuits: A survey of recent results and open questions , 2010, Found. Trends Theor. Comput. Sci..
[38] Dan Suciu,et al. Journal of the ACM , 2006 .
[39] Satyanarayana V. Lokam,et al. Efficient Reconstruction of Random Multilinear Formulas , 2011, 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science.
[40] Carsten Lund,et al. Algebraic methods for interactive proof systems , 1990, Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science.
[41] V. Vinay,et al. Arithmetic Circuits: A Chasm at Depth Four , 2008, 2008 49th Annual IEEE Symposium on Foundations of Computer Science.
[42] Neeraj Kayal,et al. Polynomial Identity Testing for Depth 3 Circuits , 2006, Computational Complexity Conference.
[43] Ilya Volkovich,et al. Deterministic identity testing of depth-4 multilinear circuits with bounded top fan-in , 2010, STOC '10.
[44] R. Raz. Multilinear-NC 1 != Multilinear-NC 2 , 2004, FOCS 2004.
[45] Ilya Volkovich,et al. Improved Polynomial Identity Testing for Read-Once Formulas , 2009, APPROX-RANDOM.
[46] Pascal Koiran,et al. The complexity of two problems on arithmetic circuits , 2007, Theor. Comput. Sci..
[47] Daniel A. Spielman,et al. Randomness efficient identity testing of multivariate polynomials , 2001, STOC '01.
[48] Jacob T. Schwartz,et al. Fast Probabilistic Algorithms for Verification of Polynomial Identities , 1980, J. ACM.
[49] Salil P. Vadhan,et al. Checking polynomial identities over any field: towards a derandomization? , 1998, STOC '98.
[50] Ilya Volkovich,et al. Black-Box Identity Testing of Depth-4 Multilinear Circuits , 2011, Combinatorica.