On computing the determinant in small parallel time using a small number of processors
Information Processing Letters
A complexity theory based on Boolean algebra
Journal of the ACM (JACM)
Irreducibility of multivariate polynomials
Journal of Computer and System Sciences
Factoring sparse multivariate polynomials
Journal of Computer and System Sciences
Uniform closure properties of P-computable functions
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Logarithmic depth circuits for algebraic functions
SIAM Journal on Computing
Parallel arithmetic computations: a survey
Proceedings of the 12th symposium on Mathematical foundations of computer science 1986
The Parallel Evaluation of General Arithmetic Expressions
Journal of the ACM (JACM)
Probabilistic Algorithms for Deciding Equivalence of Straight-Line Programs
Journal of the ACM (JACM)
Fast parallel calculation of the rank of matrices over a field of arbitrary characteristic
FCT '85 Fundamentals of Computation Theory
Completeness classes in algebra
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
Very Fast Parallel Matrix and Polynomial Arithmetic
SFCS '84 Proceedings of the 25th Annual Symposium onFoundations of Computer Science, 1984
The equivalence problem for regular expressions with squaring requires exponential space
SWAT '72 Proceedings of the 13th Annual Symposium on Switching and Automata Theory (swat 1972)
On Implications between P-NP-Hypotheses: Decision versus Computation in Algebraic Complexity
MFCS '01 Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science
Complete Problems for Valiant's Class of qp-Computable Families of Polynomials
COCOON '01 Proceedings of the 7th Annual International Conference on Computing and Combinatorics
Derandomizing polynomial identity tests means proving circuit lower bounds
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Fast computation of discrete invariants associated to a differential rational mapping
Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
Multi-linear formulas for permanent and determinant are of super-polynomial size
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Derandomizing polynomial identity tests means proving circuit lower bounds
Computational Complexity
Improved construction for universality of determinant and permanent
Information Processing Letters
Characterizing Valiant's algebraic complexity classes
Journal of Complexity
Elusive functions and lower bounds for arithmetic circuits
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Multi-linear formulas for permanent and determinant are of super-polynomial size
Journal of the ACM (JACM)
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
Arithmetic Circuits: A survey of recent results and open questions
Foundations and Trends® in Theoretical Computer Science
Succinct algebraic branching programs characterizing non-uniform complexity classes
FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
Characterizing valiant's algebraic complexity classes
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
On Enumerating Monomials and Other Combinatorial Structures by Polynomial Interpolation
Theory of Computing Systems
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An account of Valiant's theory of p-computable versus p-definable polynomials, an arithmetic analogue of the Boolean theory of P versus NP, is presented, with detailed proofs of Valiant's central results.