Derandomizing Polynomial Identity Tests Means Proving Circuit Lower Bounds
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[1] Avi Wigderson,et al. Randomness vs. time: de-randomization under a uniform assumption , 1998, Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280).
[2] Rafael Hirschfeld,et al. Pseudorandom Generators and Complexity Classes , 1989, Advances in Computational Research.
[3] Marek Karpinski,et al. On Zero-Testing and Interpolation of k-Sparse Multivariate Polynomials Over Finite Fields , 1991, Theor. Comput. Sci..
[4] Zhi-Zhong Chen,et al. Reducing randomness via irrational numbers , 1997, STOC '97.
[5] José D. P. Rolim,et al. A new general derandomization method , 1998, JACM.
[6] K. Ramachandra,et al. Vermeidung von Divisionen. , 1973 .
[7] Michael E. Saks,et al. Exponential lower bounds for depth 3 Boolean circuits , 1997, STOC '97.
[8] Stephen A. Cook,et al. Efficiently Approximable Real-Valued Functions , 2000, Electron. Colloquium Comput. Complex..
[9] Erich Kaltofen,et al. Greatest common divisors of polynomials given by straight-line programs , 1988, JACM.
[10] Marek Karpinski,et al. Fast Parallel Algorithms for Sparse Multivariate Polynomial Interpolation over Finite Fields , 1988, SIAM J. Comput..
[11] László Lovász,et al. Interactive proofs and the hardness of approximating cliques , 1996, JACM.
[12] Journal of the Association for Computing Machinery , 1961, Nature.
[13] Ran Raz,et al. A sub-constant error-probability low-degree test, and a sub-constant error-probability PCP characterization of NP , 1997, STOC '97.
[14] Manuel Blum,et al. Equivalence of Free Boolean Graphs can be Decided Probabilistically in Polynomial Time , 1980, Inf. Process. Lett..
[15] Manuel Blum,et al. Designing programs that check their work , 1989, STOC '89.
[16] Lance Fortnow,et al. One-sided Versus Two-sided Error in Probabilistic Computation , 1999, STACS.
[17] Leslie G. Valiant,et al. The Complexity of Computing the Permanent , 1979, Theor. Comput. Sci..
[18] Lance Fortnow,et al. Nonrelativizing separations , 1998, Proceedings. Thirteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat. No.98CB36247).
[19] Carsten Lund,et al. Algebraic methods for interactive proof systems , 1990, Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science.
[20] Manindra Agrawal,et al. PRIMES is in P , 2004 .
[21] Ronitt Rubinfeld,et al. Robust Characterizations of Polynomials with Applications to Program Testing , 1996, SIAM J. Comput..
[22] Richard P. Brent,et al. The Parallel Evaluation of General Arithmetic Expressions , 1974, JACM.
[23] Richard J. Lipton,et al. A Probabilistic Remark on Algebraic Program Testing , 1978, Inf. Process. Lett..
[24] Avi Wigderson,et al. In search of an easy witness: exponential time vs. probabilistic polynomial time , 2001, Proceedings 16th Annual IEEE Conference on Computational Complexity.
[25] Erich Kaltofen,et al. On computing determinants of matrices without divisions , 1992, ISSAC '92.
[26] Richard J. Lipton,et al. New Directions In Testing , 1989, Distributed Computing And Cryptography.
[27] Madhu Sudan,et al. Highly Resilient Correctors for Polynomials , 1992, Inf. Process. Lett..
[28] Leslie G. Valiant,et al. Completeness classes in algebra , 1979, STOC.
[29] Vaughan R. Pratt,et al. Every Prime has a Succinct Certificate , 1975, SIAM J. Comput..
[30] Madhu Sudan,et al. Decoding of Reed Solomon Codes beyond the Error-Correction Bound , 1997, J. Complex..
[31] Alexander A. Razborov,et al. Natural Proofs , 2007 .
[32] László Babai,et al. Trading group theory for randomness , 1985, STOC '85.
[33] Noam Nisan,et al. Constant depth circuits, Fourier transform, and learnability , 1989, 30th Annual Symposium on Foundations of Computer Science.
[34] Noam Nisan,et al. BPP has subexponential time simulations unless EXPTIME has publishable proofs , 1991, [1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference.
[35] László Lovász,et al. On determinants, matchings, and random algorithms , 1979, FCT.
[36] Manindra Agrawal,et al. Primality and identity testing via Chinese remaindering , 1999, 40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039).
[37] KaltofenErich. Greatest common divisors of polynomials given by straight-line programs , 1988 .
[38] Avi Wigderson,et al. Extractors and pseudo-random generators with optimal seed length , 2000, STOC '00.
[39] Ran Raz,et al. Extracting all the randomness and reducing the error in Trevisan's extractors , 1999, STOC '99.
[40] Samuel R. Buss,et al. An Optimal Parallel Algorithm for Formula Evaluation , 1992, SIAM J. Comput..
[41] Richard Zippel,et al. Probabilistic algorithms for sparse polynomials , 1979, EUROSAM.
[42] Avi Wigderson,et al. P = BPP if E requires exponential circuits: derandomizing the XOR lemma , 1997, STOC '97.
[43] Vijay V. Vazirani,et al. Matching is as easy as matrix inversion , 1987, STOC.
[44] Michael E. Saks,et al. An improved exponential-time algorithm for k-SAT , 2005, JACM.
[45] Daniel A. Spielman,et al. Randomness efficient identity testing of multivariate polynomials , 2001, STOC '01.
[46] Jacob T. Schwartz,et al. Fast Probabilistic Algorithms for Verification of Polynomial Identities , 1980, J. ACM.
[47] Joachim von zur Gathen,et al. Feasible Arithmetic Computations: Valiant's Hypothesis , 1987, J. Symb. Comput..
[48] Salil P. Vadhan,et al. Checking polynomial identities over any field: towards a derandomization? , 1998, STOC '98.
[49] Christopher Umans. Pseudo-random generators for all hardnesses , 2002, STOC '02.
[50] Noam Nisan,et al. Hardness vs Randomness , 1994, J. Comput. Syst. Sci..
[51] Carsten Lund,et al. Proof verification and hardness of approximation problems , 1992, Proceedings., 33rd Annual Symposium on Foundations of Computer Science.
[52] Joan Feigenbaum,et al. Hiding Instances in Multioracle Queries , 1990, STACS.
[53] Ron M. Roth,et al. Interpolation and Approximation of Sparse Multivariate Polynomials over GF(2) , 1991, SIAM J. Comput..
[54] Adi Shamir,et al. IP = PSPACE , 1992, JACM.
[55] Oded Goldreich,et al. Another proof that bpp?ph (and more) , 1997 .
[56] Seinosuke Toda,et al. PP is as Hard as the Polynomial-Time Hierarchy , 1991, SIAM J. Comput..
[57] Avi Wigderson,et al. Near-optimal conversion of hardness into pseudo-randomness , 1999, 40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039).
[58] PaturiRamamohan,et al. An improved exponential-time algorithm for k-SAT , 2005 .
[59] Luca Trevisan,et al. Pseudorandom generators without the XOR lemma , 1999, Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317).
[60] Aravind Srinivasan,et al. Randomness-optimal unique element isolation, with applications to perfect matching and related problems , 1993, SIAM J. Comput..
[61] Avi Wigderson,et al. Randomness vs Time: Derandomization under a Uniform Assumption , 2001, J. Comput. Syst. Sci..
[62] Andrew Chi-Chih Yao,et al. Theory and Applications of Trapdoor Functions (Extended Abstract) , 1982, FOCS.
[63] Aravind Srinivasan,et al. Randomness-Optimal Unique Element Isolation with Applications to Perfect Matching and Related Problems , 1995, SIAM J. Comput..
[64] Carsten Lund,et al. Non-deterministic exponential time has two-prover interactive protocols , 2005, computational complexity.
[65] Erich Kaltofen,et al. Factorization of Polynomials Given by Straight-Line Programs , 1989, Adv. Comput. Res..
[66] Madhu Sudan,et al. Improved Low-Degree Testing and its Applications , 1997, STOC '97.
[67] Ramamohan Paturi,et al. Circuits, cnfs, and satisfiability , 1998 .
[68] Sanjeev Arora,et al. Probabilistic checking of proofs: a new characterization of NP , 1998, JACM.
[69] Leslie G. Valiant,et al. NP is as easy as detecting unique solutions , 1985, STOC '85.
[70] Valentine Kabanets,et al. Easiness assumptions and hardness tests: trading time for zero error , 2000, Proceedings 15th Annual IEEE Conference on Computational Complexity.
[71] Dieter van Melkebeek,et al. Graph Nonisomorphism Has Subexponential Size Proofs Unless the Polynomial-Time Hierarchy Collapses , 2002, SIAM J. Comput..
[72] Avi Wigderson,et al. In search of an easy witness: exponential time vs. probabilistic polynomial time , 2002, J. Comput. Syst. Sci..
[73] László Babai,et al. Arthur-Merlin Games: A Randomized Proof System, and a Hierarchy of Complexity Classes , 1988, J. Comput. Syst. Sci..
[74] Alexander L. Chistov,et al. Fast parallel calculation of the rank of matrices over a field of arbitrary characteristic , 1985, FCT.
[75] Michael E. Saks,et al. Exponential lower bounds for depth three Boolean circuits , 2000, computational complexity.
[76] Pavel Pudlák,et al. Satisfiability Coding Lemma , 1997, Proceedings 38th Annual Symposium on Foundations of Computer Science.
[77] Christopher Umans,et al. Simple extractors for all min-entropies and a new pseudo-random generator , 2001, Proceedings 2001 IEEE International Conference on Cluster Computing.
[78] Oscar H. Ibarra,et al. Probabilistic Algorithms for Deciding Equivalence of Straight-Line Programs , 1983, JACM.