Parallel algorithms for algebraic problems
SIAM Journal on Computing
A taxonomy of problems with fast parallel algorithms
Information and Control
Relativized circuit complexity
Journal of Computer and System Sciences
Introduction to finite fields and their applications
Introduction to finite fields and their applications
Information and Computation
Very fast parallel polynomial arithmetic
SIAM Journal on Computing
Boolean circuits versus arithmetic circuits
Information and Computation
A note on enumerative counting
Information Processing Letters
Inverting a Vandermonde matrix in minimum parallel time
Information Processing Letters
Limits to parallel computation: P-completeness theory
Limits to parallel computation: P-completeness theory
Information and Computation
Polynomial-time Membership Comparable Sets
SIAM Journal on Computing
Reconstructing Algebraic Functions from Mixed Data
SIAM Journal on Computing
Modern computer algebra
Tally NP sets and easy census functions
Information and Computation
Journal of Computer and System Sciences
Resolution of Hartmanis' conjecture for NL-hard sparse sets
Theoretical Computer Science - computing and combinatorics
Introduction to Coding Theory
Polynomial Factorization 1987-1991
LATIN '92 Proceedings of the 1st Latin American Symposium on Theoretical Informatics
On Finding the Number of Graph Automorphisms
On Finding the Number of Graph Automorphisms
The circuit value problem is log space complete for P
ACM SIGACT News
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We show that one cannot rule out even a single possibility for the value of an arithmetic circuit on a given input using an NC algorithm, unless P collapses to NC (i.e., unless all problems with polynomial-time sequential solutions can be efficiently parallelized). In other words, excluding any possible solution in this case is as hard as actually finding the solution. The result is robust with respect to NC algorithms that err (i.e., exclude the correct value) with small probability. We also show that P collapses all the way down to NC1 when the characteristic of the field that the problem is over is sufficiently large (but in this case under a stronger elimination hypothesis that depends on the characteristic).