Polynomial Identity Testing for Depth 3 Circuits
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
Derandomizing the Isolation Lemma and Lower Bounds for Circuit Size
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Multi-linear formulas for permanent and determinant are of super-polynomial size
Journal of the ACM (JACM)
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
On Lower Bounds for Constant Width Arithmetic Circuits
ISAAC '09 Proceedings of the 20th International Symposium 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 hardness of the noncommutative determinant
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
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part I
Hardness-Randomness Tradeoffs for Bounded Depth Arithmetic Circuits
SIAM Journal on 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
Algebraic proofs over noncommutative formulas
Information and Computation
Algorithms for testing monomials in multivariate polynomials
COCOA'11 Proceedings of the 5th international conference on Combinatorial optimization and applications
Algebraic proofs over noncommutative formulas
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
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
Reconstruction of depth-4 multilinear circuits with top fan-in 2
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Journal of Combinatorial Optimization
Quasi-polynomial hitting-set for set-depth-Δ formulas
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
On testing monomials in multivariate polynomials
Theoretical Computer Science
Non-commutative arithmetic circuits with division
Proceedings of the 5th conference on Innovations in theoretical computer science
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We give a deterministic polynomial time algorithm for polynomial identity testing in the following two cases: Non-commutative arithmetic formulas: The algorithm gets as an input an arithmetic formula in the non-commuting variables x1,···,xn and determines whether or not the output of the formula is identically 0 (as a formal expression) Pure arithmetic circuits: The algorithm gets as an input a pure set-multilinear arithmetic circuit (as defined by Nisan and Wigderson) in the variables x1,···,xn and determines whether or not the output of the circuit is identically 0 (as a formal expression).One application is a deterministic polynomial time identity testing for set-multilinear arithmetic circuits of depth 3. We also give a deterministic polynomial time identity testing algorithm for non-commutative algebraic branching programs as defined by Nisan. Finally, we obtain an exponential lower bound for the size of pure setmultilinear arithmetic circuits for the permanent and for the determinant. (Only lower bounds for the depth of pure circuits were previously known.)