Simulating probabilistic by deterministic algebraic computation trees
Theoretical Computer Science
Lower bounds for the approximative complexity
Theoretical Computer Science
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Feasible arithmetic computations: Valiant's hypothesis
Journal of Symbolic Computation
Fast algorithms for N-dimensional restrictions of hard problems
Journal of the ACM (JACM)
Complexity measures for public-key cryptosystems
SIAM Journal on Computing - Special issue on cryptography
Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Test complexity of generic polynomials
Journal of Complexity
On randomized semi-algebraic test complexity
Journal of Complexity
Point location in arrangements of hyperplanes
Information and Computation
On the intrinsic complexity of elimination theory
Journal of Complexity - Special issue: invited articles dedicated to J. F. Traub on the occasion of his 60th birthday
Computing over the reals with addition and order
Selected papers of the workshop on Continuous algorithms and complexity
On real Turing machines that toss coins
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
A weak version of the Blum, Shub, and Smale model
Journal of Computer and System Sciences - Special issue: dedicated to the memory of Paris Kanellakis
Randomized Ω(n2) lower bound for knapsack
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Complexity and real computation
Complexity and real computation
Simplified lower bounds for polynomials with algebraic coefficients
Journal of Complexity
Are lower bounds easier over the reals?
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
A deterministic strongly polynomial algorithm for matrix scaling and approximate permanents
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Random Structures & Algorithms
A Polynomial Linear Search Algorithm for the n-Dimensional Knapsack Problem
Journal of the ACM (JACM)
Time-space tradeoffs in algebraic complexity theory
Journal of Complexity
Cook's versus Valiant's hypothesis
Theoretical Computer Science - Selected papers in honor of Manuel Blum
On lower bounds for the complexity of polynomials and their multiples
Computational Complexity
Completeness classes in algebra
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
Algebraic Complexity Theory
Some Remarks on the L-Conjecture
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
VPSPACE and a transfer theorem over the complex field
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
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Several models of NP-completeness in an algebraic framework of computation have been proposed in the past, each of them hinging on a fundamental hypothesis of type P≠NP. We first survey some known implications between such hypotheses and then describe attempts to establish further connections. This leads us to the problem of relating the complexity of computational and decisional tasks and naturally raises the question about the connection of the complexity of a polynomial with those of its factors. After reviewing what is known with this respect, we discuss a new result involving a concept of approximative complexity.