Algebraic Decompositions
Kernel extraction
Semi-algebraic division
Resubstitution
Factoring/Decomposition
[-q]: Two-cube divisors
[-g]: Best divisors
mvsis> fx [-q] [-g]
mvsis> resub
mvsis> decomp
mvsis> factor
F = a
{0,1,2}
c
{3}
+ b
{1,2,3}
c
{3}
+ a
{0}
b
{1,2,3}
c
{0}
+a
{0}
c
{1}
= (c
{3}
+a
{0}
c
{0,1}
)
(a
{0,1,2}
c
{1,3}
+b
{1,2,3}
c
{0,3}
)
F
M. Gao and R. K. Brayton, “Multi-valued Multi-level Network Decomposition”,
IWLS, June 2001.
Example: factoring/
decomposition/resub
The optimization sequence is:
1.
Derive the kernel/cubes;
2.
Divide it into the original expressions;
3.
Substitute into other expressions;
Different flavors of commands developed around this concept, like in SIS.