Finding irreducible polynomials over finite fields
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
A deterministic algorithm for sparse multivariate polynomial interpolation
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Fast parallel algorithms for sparse multivariate polynomial interpolation over finite fields
SIAM Journal on Computing
On zero-testing and interpolation of k -sparse multivariate polynomials over finite fields
Theoretical Computer Science
Learning sparse multivariate polynomials over a field with queries and counterexamples
Journal of Computer and System Sciences
On some approximation problems concerning sparse polynomials over finite fields
Theoretical Computer Science - Special issue on complexity theory and the theory of algorithms as developed in the CIS
Reducing randomness via irrational numbers
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Checking polynomial identities over any field: towards a derandomization?
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Fast Probabilistic Algorithms for Verification of Polynomial Identities
Journal of the ACM (JACM)
Randomness efficient identity testing of multivariate polynomials
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Probabilistic algorithms for sparse polynomials
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
Primality and identity testing via Chinese remaindering
Journal of the ACM (JACM)
Testing polynomials which are easy to compute (Extended Abstract)
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
Deterministic polynomial identity testing in non-commutative models
Computational Complexity
Derandomizing polynomial identity tests means proving circuit lower bounds
Computational Complexity
Polynomial Identity Testing for Depth 3 Circuits
Computational Complexity
Locally Decodable Codes with Two Queries and Polynomial Identity Testing for Depth 3 Circuits
SIAM Journal on Computing
CCC '08 Proceedings of the 2008 IEEE 23rd Annual Conference on Computational Complexity
Diagonal Circuit Identity Testing and Lower Bounds
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Arithmetic Circuits: A Chasm at Depth Four
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
An Almost Optimal Rank Bound for Depth-3 Identities
CCC '09 Proceedings of the 2009 24th Annual IEEE Conference on Computational Complexity
Reconstruction of Generalized Depth-3 Arithmetic Circuits with Bounded Top Fan-in
CCC '09 Proceedings of the 2009 24th Annual IEEE Conference on Computational Complexity
Improved Polynomial Identity Testing for Read-Once Formulas
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Blackbox Polynomial Identity Testing for Depth 3 Circuits
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
The monomial ideal membership problem and polynomial identity testing
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Deterministic identity testing of depth-4 multilinear circuits with bounded top fan-in
Proceedings of the forty-second ACM symposium on Theory of computing
Tensor-rank and lower bounds for arithmetic formulas
Proceedings of the forty-second ACM symposium on Theory of computing
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Arithmetic Circuits: A survey of recent results and open questions
Foundations and Trends® in Theoretical Computer Science
Black-box identity testing of depth-4 multilinear circuits
Proceedings of the forty-third annual ACM symposium on Theory of computing
Derandomizing Polynomial Identity Testing for Multilinear Constant-Read Formulae
CCC '11 Proceedings of the 2011 IEEE 26th Annual Conference on Computational Complexity
Proving lower bounds via pseudo-random generators
FSTTCS '05 Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science
Algebraic independence and blackbox identity testing
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
On identity testing of tensors, low-rank recovery and compressed sensing
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Algebraic independence and blackbox identity testing
Information and Computation
Quasi-polynomial hitting-set for set-depth-Δ formulas
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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Let C be a depth-3 circuit with n variables, degree d and top fanin k (called ΣΠΣ(k,d,n) circuits) over base field FF. It is a major open problem to design a deterministic polynomial time blackbox algorithm that tests if C is identically zero. Klivans & Spielman (STOC 2001) observed that the problem is open even when k is a constant. This case has been subjected to a serious study over the past few years, starting from the work of Dvir & Shpilka (STOC 2005). We give the first polynomial time blackbox algorithm for this problem. Our algorithm runs in time poly(n)dk, regardless of the base field. The only field for which polynomial time algorithms were previously known is FF = QQ (Kayal & Saraf, FOCS 2009, and Saxena & Seshadhri, FOCS 2010). This is the first blackbox algorithm for depth-$3$ circuits that does not use the rank based approaches of Karnin & Shpilka (CCC 2008). We prove an important tool for the study of depth-3 identities. We design a blackbox polynomial time transformation that reduces the number of variables in a ΣΠΣ(k,d,n) circuit to k variables, but preserves the identity structure.