Log depth circuits for division and related problems
SIAM Journal on Computing
Handbook of theoretical computer science (vol. A)
Complexity classes defined by counting quantifiers
Journal of the ACM (JACM)
On threshold circuits and polynomial computation
SIAM Journal on Computing
Complexity and real computation
Complexity and real computation
Cook's versus Valiant's hypothesis
Theoretical Computer Science - Selected papers in honor of Manuel Blum
Introduction to Circuit Complexity: A Uniform Approach
Introduction to Circuit Complexity: A Uniform Approach
Uniform constant-depth threshold circuits for division and iterated multiplication
Journal of Computer and System Sciences - Complexity 2001
Straight-line complexity and integer factorization
ANTS-I Proceedings of the First International Symposium on Algorithmic Number Theory
Completeness classes in algebra
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
Valiant's model and the cost of computing integers
Computational Complexity
On the Complexity of Numerical Analysis
CCC '06 Proceedings of the 21st Annual IEEE Conference on Computational Complexity
Algebraic Complexity Theory
Kolmogorov Complexity Theory over the Reals
Electronic Notes in Theoretical Computer Science (ENTCS)
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Let τ (n) denote the minimum number of arithmetic operations sufficient to build the integer n from the constant 1.We prove that if there are arithmetic circuits for computing the permanent of n by n matrices having size polynomial in n, then τ(n!) is polynomially bounded in log n. Under the same assumption on the permanent, we conclude that the Pochhammer-Wilkinson polynomials Πk=1n (X - k) and the Taylor approximations Σk=0n 1/k! Xk and Σk=1n 1/kXk of exp and log, respectively, can be computed by arithmetic circuits of size polynomial in log n (allowing divisions). This connects several so far unrelated conjectures in algebraic complexity.