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by Zeljko Zilic, Zvonko G. Vranesic
http://www.eecg.toronto.edu/~zeljko/PolyRM.ps.Z
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Abstract:
This paper presents new algorithms for the sparse multivariate polynomial interpolation over finite fields, which can be used for optimizing Reed-Muller forms for MVL functions. Starting with a new quadratic time interpolation algorithm for Boolean functions, we develop a method that decomposes the problem into several smaller problems for the MVL case. We then show how each of these problems can be solved by a practical probabilistic algorithm. The approach is extended to fixed polarity RM forms, in which the complexity of the resulting forms becomes simpler and also the running time of the algorithm is reduced. 1
Citations
|
80
|
Effective Polynomial Computation
– Zippel
- 1993
|
|
48
|
ªApplications of Boolean Algebra to Switching Circuit Design and to Error Detection,º
– Muller
- 1954
|
|
43
|
Fast parallel algorithms for sparse multivariate polynomial interpolation over finite fields
– Grigoriev, Karpinski, et al.
- 1990
|
|
40
|
Interpolating polynomials from their values
– Zippel
- 1990
|
|
32
|
ªA Class of Multiple-Error-Correcting Codes and the Decoding Scheme,º
– Reed
- 1954
|
|
31
|
Computational aspects of polynomial interpolation in several variables
– Boor, Ron
- 1992
|
|
18
|
Interpolation and approximation of sparse multivariate polynomials over GF (2
– Roth, Benedek
- 1991
|
|
10
|
Multivariate polynomial interpolation
– Gasca, Sauer
- 1990
|
|
8
|
Computation of Reed-Muller expansions of incompletely specified Boolean functions from reduced representations
– Varma, Trachtenberg
- 1991
|
|
6
|
Reed-Muller expansions of incompletely specified functions
– Green
- 1987
|
|
5
|
Optimisation of Reed-Muller logic functions
– McKenzie, Almaini, et al.
- 1993
|
|
4
|
Applying coding theory to sparse interpolation
– Dur, Grabmeier
- 1993
|
|
4
|
A multiple-valued ReedMuller transform for incompletely specified functions
– Zilic, Vranesic
- 1995
|
|
3
|
A deterministic algorithm for sparse multivariate polynomial interpolation
– Or, M, et al.
- 1988
|
|
2
|
A Multiple Valued Reed-Muller Transforms for Incompletely Specified Functions, accepted for publication in
– Zilic, Vranesic
- 1994
|
|
1
|
A transform for logic networks
– Jr
- 1969
|
