Random Arithmetic Formulas Can Be Reconstructed Efficiently
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[1] Gerhard Pfister,et al. Primary Decomposition: Algorithms and Comparisons , 1997, Algorithmic Algebra and Number Theory.
[2] David A. Cox,et al. Ideals, Varieties, and Algorithms , 1997 .
[3] Amir Yehudayoff,et al. Arithmetic Circuits: A survey of recent results and open questions , 2010, Found. Trends Theor. Comput. Sci..
[4] Erich Kaltofen,et al. Computing with polynomials given by straight-line programs II sparse factorization , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).
[5] Satyanarayana V. Lokam,et al. Efficient Reconstruction of Random Multilinear Formulas , 2011, 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science.
[6] M. Ben-Or,et al. A Deterministic Algorithm for Sparse Multivariate Polynominal Interpolation (Extended Abstract) , 1988, Symposium on the Theory of Computing.
[7] Daniel Lazard,et al. Thirty years of Polynomial System Solving, and now? , 2009, J. Symb. Comput..
[8] Nader H. Bshouty,et al. Size-depth tradeoffs for algebraic formulae , 1991, [1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science.
[9] Stasys Jukna,et al. Boolean Function Complexity Advances and Frontiers , 2012, Bull. EATCS.
[10] Amir Shpilka. Interpolation of Depth-3 Arithmetic Circuits with Two Multiplication Gates , 2009, SIAM J. Comput..
[11] J. Kollár. Sharp effective Nullstellensatz , 1988 .
[12] Satyanarayana V. Lokam,et al. Reconstruction of depth-4 multilinear circuits with top fan-in 2 , 2012, STOC '12.
[13] Eyal Kushilevitz,et al. Learning functions represented as multiplicity automata , 2000, JACM.
[14] Vikraman Arvind,et al. New Results on Noncommutative and Commutative Polynomial Identity Testing , 2008, 2008 23rd Annual IEEE Conference on Computational Complexity.
[15] Neeraj Kayal,et al. Approaching the Chasm at Depth Four , 2013, Computational Complexity Conference.
[16] Neeraj Kayal,et al. Affine projections of polynomials , 2011, Electron. Colloquium Comput. Complex..
[17] Joe W. Harris,et al. Algebraic Geometry: A First Course , 1995 .
[18] Erich Kaltofen,et al. Computing with Polynomials Given By Black Boxes for Their Evaluations: Greatest Common Divisors, Factorization, Separation of Numerators and Denominators , 1990, J. Symb. Comput..
[19] Erich Kaltofen,et al. Improved Sparse Multivariate Polynomial Interpolation Algorithms , 1988, ISSAC.
[20] Michael E. Saks,et al. Minimizing Disjunctive Normal Form Formulas and AC0 Circuits Given a Truth Table , 2008, SIAM J. Comput..
[21] Erich Kaltofen,et al. Factorization of Polynomials Given by Straight-Line Programs , 1989, Adv. Comput. Res..
[22] Linda Sellie,et al. Exact learning of random DNF over the uniform distribution , 2009, STOC '09.
[23] Teo Mora,et al. Local Decomposition Algorithms , 1990, AAECC.
[24] Yishay Mansour,et al. Learning Boolean Functions via the Fourier Transform , 1994 .
[25] Thomas W. Dubé. A Combinatorial Proof of the Effective Nullstellensatz , 1993, J. Symb. Comput..
[26] Nader H. Bshouty,et al. Interpolating Arithmetic Read-Once Formulas in Parallel , 1998, SIAM J. Comput..
[27] Juan Sabia,et al. Effective equidimensional decomposition of affine varieties , 2002 .
[28] Daniel A. Spielman,et al. Randomness efficient identity testing of multivariate polynomials , 2001, STOC '01.
[29] Gian-Carlo Rota,et al. Apolarity and Canonical Forms for Homogeneous Polynomials , 1993, Eur. J. Comb..
[30] Chee-Keng Yap,et al. Fundamental problems of algorithmic algebra , 1999 .
[31] Adam R. Klivans,et al. Learning Arithmetic Circuits via Partial Derivatives , 2003, COLT.
[32] Daniel Lazard,et al. Solving systems of algebraic equations , 2001, SIGS.
[33] Johan Håstad. Tensor Rank is NP-Complete , 1990, J. Algorithms.
[34] Erich Kaltofen,et al. Polynomial-Time Reductions from Multivariate to Bi- and Univariate Integral Polynomial Factorization , 1985, SIAM J. Comput..
[35] Heinz Kredel,et al. Gröbner Bases: A Computational Approach to Commutative Algebra , 1993 .
[36] Neeraj Kayal,et al. Efficient algorithms for some special cases of the polynomial equivalence problem , 2011, SODA '11.
[37] David Buchfuhrer,et al. The Complexity of Boolean Formula Minimization , 2008, ICALP.
[38] Matthias Aschenbrenner. Ideal membership in polynomial rings over the integers , 2003, math/0305172.
[39] Lance Fortnow,et al. Efficient Learning Algorithms Yield Circuit Lower Bounds , 2006, COLT.
[40] Andrew Wan,et al. Mansour's Conjecture is True for Random DNF Formulas , 2010, COLT.
[41] G. Greuel,et al. A Singular Introduction to Commutative Algebra , 2002 .
[42] K. Kalorkoti,et al. A Lower Bound for the Formula Size of Rational Functions , 1982, SIAM J. Comput..
[43] Neeraj Kayal,et al. An exponential lower bound for homogeneous depth four arithmetic circuits with bounded bottom fanin , 2012, Electron. Colloquium Comput. Complex..
[44] Jin-Yi Cai,et al. Circuit minimization problem , 2000, STOC '00.
[45] Neeraj Kayal. Affine projections of polynomials: extended abstract , 2012, STOC '12.
[46] Amir Shpilka,et al. Reconstruction of Generalized Depth-3 Arithmetic Circuits with Bounded Top Fan-in , 2009, 2009 24th Annual IEEE Conference on Computational Complexity.
[47] Richard Zippel,et al. Interpolating Polynomials from Their Values , 1990, J. Symb. Comput..
[48] David A. Cox,et al. Using Algebraic Geometry , 1998 .
[49] Grete Hermann,et al. The question of finitely many steps in polynomial ideal theory , 1998, SIGS.
[50] Grete Hermann,et al. Die Frage der endlich vielen Schritte in der Theorie der Polynomideale , 1926 .
[51] Teresa Krick,et al. Membership problem, Representation problem and the Computation of the Radical for one-dimensional Ideals , 1991 .
[52] T. Mignon,et al. A quadratic bound for the determinant and permanent problem , 2004 .
[53] Daniel Lazard,et al. Resolution des Systemes d'Equations Algebriques , 1981, Theor. Comput. Sci..
[54] Joachim von zur Gathen. Permanent and determinant , 1987 .