Elusive functions and lower bounds for arithmetic circuits
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Arithmetic Circuits, Syntactic Multilinearity, and the Limitations of Skew Formulae
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
Lower Bounds for the Determinantal Complexity of Explicit Low Degree Polynomials
CSR '09 Proceedings of the Fourth International Computer Science Symposium in Russia on Computer Science - Theory and Applications
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
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
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
On the incompressibility of monotone DNFs
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
Balancing bounded treewidth circuits
CSR'10 Proceedings of the 5th international conference on Computer Science: theory and Applications
Separating multilinear branching programs and formulas
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Balancing Bounded Treewidth Circuits
Theory of Computing Systems
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An arithmetic circuit or formula is multilinear if the polynomial computed at each of its wires is multilinear. We give an explicit example for a polynomial f(x1, ..., xn), with coefficients in {0, 1}, such that over any field: 1. f can be computed by a polynomial-size multilinear circuit of depth O(log虏 n). 2. Any multilinear formula for f is of size n^{\Omega (\log n)}. This gives a super-polynomial gap between multilinear circuit and formula size, and separates multilinear NC驴 circuits from multilinear NC驴 circuits.