Parallel solution of certain toeplitz linear systems
SIAM Journal on Computing
Parallel computation for well-endowed rings and space-bounded probabilistic machines
Information and Control
Parallel algorithms for algebraic problems
SIAM Journal on Computing
A taxonomy of problems with fast parallel algorithms
Information and Control
Polynomial division and its computational complexity
Journal of Complexity
Logarithmic depth circuits for algebraic functions
SIAM Journal on Computing
Log depth circuits for division and related problems
SIAM Journal on Computing
Parallel arithmetic computations: a survey
Proceedings of the 12th symposium on Mathematical foundations of computer science 1986
SIAM Journal on Computing
The parallel complexity of exponentiating polynomials over finite fields
Journal of the ACM (JACM)
Factoring Polynomials over Algebraic Number Fields
SIAM Journal on Computing
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Litow & Davida (1988) show that inverses in large finite fields of small characteristicp, say p=2, can be computed by Boolean circuits of (order-optimal) logarithmic depth. We note that their numerical approach can also be implemented purely algebraically, and that the resulting much simpler algorithm yields, also for large p, both arithmetic and Boolean reductions of inversion in F"p"n to inversion in F"p.