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
Algebraic independence and blackbox identity testing
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
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
Testers and their applications
Proceedings of the 5th conference on Innovations in theoretical computer science
On Enumerating Monomials and Other Combinatorial Structures by Polynomial Interpolation
Theory of Computing Systems
Monomials, multilinearity and identity testing in simple read-restricted circuits
Theoretical Computer Science
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We present a polynomial-time deterministic algorithm for testing whether constant-read multilinear arithmetic formulae are identically zero. In such a formula each variable occurs only a constant number of times and each subformula computes a multilinear polynomial. Before our work no subexponential-time deterministic algorithm was known for this class of formulae. We also present a deterministic algorithm that works in a blackbox fashion and runs in quasi-polynomial time in general, and polynomial time for constant depth. Finally, we extend our results and allow the inputs to be replaced with sparse polynomials. Our results encompass recent deterministic identity tests for sums of a constant number of read-once formulae, and for multilinear depth-four circuits.