Introduction to finite fields and their applications
Introduction to finite fields and their applications
A direct version of Shamir and Snir's lower bounds on monotone circuit depth
Information Processing Letters
Checking polynomial identities over any field: towards a derandomization?
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
An exponential lower bound for depth 3 arithmetic circuits
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)
Some Exact Complexity Results for Straight-Line Computations over Semirings
Journal of the ACM (JACM)
Reducing Randomness via Irrational Numbers
SIAM Journal on Computing
Randomness efficient identity testing of multivariate polynomials
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Lower bounds for matrix product, in bounded depth circuits with arbitrary gates
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Depth-3 arithmetic circuits over fields of characteristic zero
Computational Complexity
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)
Locally decodable codes with 2 queries and polynomial identity testing for depth 3 circuits
Proceedings of the thirty-seventh 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
Read-once polynomial identity testing
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Hardness-randomness tradeoffs for bounded depth arithmetic circuits
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
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
The ideal membership problem and polynomial identity testing
Information and Computation
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
On the relation between polynomial identity testing and finding variable disjoint factors
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Arithmetic Circuits: A survey of recent results and open questions
Foundations and Trends® in Theoretical Computer Science
Hardness-Randomness Tradeoffs for Bounded Depth Arithmetic Circuits
SIAM Journal on Computing
Black-box identity testing of depth-4 multilinear circuits
Proceedings of the forty-third annual ACM symposium on Theory of computing
Blackbox identity testing for bounded top fanin depth-3 circuits: the field doesn't matter
Proceedings of the forty-third annual ACM symposium on Theory of computing
Recent results on polynomial identity testing
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
An Almost Optimal Rank Bound for Depth-3 Identities
SIAM Journal on Computing
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Algebraic independence and blackbox identity testing
Information and Computation
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We study the identity testing problem for depth 3 arithmetic circuits ( $$\sum\prod\sum$$ circuit). We give the first deterministic polynomial time identity test for $$\sum\prod\sum$$ circuits with bounded top fanin. We also show that the rank of a minimal and simple $$\sum\prod\sum$$ circuit with bounded top fanin, computing zero, can be unbounded. These results answer the open questions posed by Klivans---Spielman (STOC 2001) and Dvir---Shpilka (STOC 2005).