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Reed–Muller expansion : ウィキペディア英語版
Reed–Muller expansion

In Boolean logic, a Reed–Muller (or Davio) expansion is a decomposition of a boolean function.
For a boolean function f(x_1,\ldots,x_n) we set with respect to x_i:
:
\begin
f_(x) & = f(x_1,\ldots,x_,1,x_,\ldots,x_n) \\()
f_(x)& = f(x_1,\ldots,x_,0,x_,\ldots,x_n) \\()
\frac & = f_(x) \oplus f_(x)\, \\
\end

as the positive and negative cofactors of f, and the boolean derivation of f.
Then we have for the Reed–Muller or positive Davio expansion:
:
f = f_ \oplus x_i \frac.

Similar to binary decision diagrams (BDDs), where nodes represent Shannon expansion with respect to the according variable, we can define a
decision diagram based on the Reed–Muller expansion. These decision diagrams are called functional BDDs (FBDDs).
==References ==

*Kebschull, U. and Rosenstiel, W., ''Efficient graph-based computation and manipulation of functional decision diagrams'', Proceedings 4th European Conference on Design Automation, 1993, pp. 278–282


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