Number of combinations at a given complexity layer
This function calculates the number of all possible combinations of conditions (including all levels for each condition), at a given complexity layer.
complexity(n, layers, noflevels)
n |
Numeric scalar, the number of input conditions. |
layers |
Numeric vector, the complexity layer(s) with values from 1 to n. |
noflevels |
Numeric vector containing the number of levels for each of the n conditions. |
These are the number of combinations which the CCubes algorithm (Dusa, 2018) checks to determine the prime implicants from a minimization process.
In the bottom-up approach, CCubes first checks for single conditions (combinations of both presence and absence, or more levels if multi-value), then all possible combinations of levels for two conditions etc.
The precise equation that partitions the search space into complexity layers is:
∑_{c = 1}^{k} {k\choose c} ∏_{s = 1}^{c} l_s
where l stands for the number of levels for each combination of c conditions out of k.
A numeric vector.
Adrian Dusa
Dusa, A. (2018) “Consistency Cubes: A Fast, Efficient Method for Boolean Minimization”, R Journal, doi: 10.32614/RJ-2018-080
complexity(3) # all layers from 1 to 3 complexity(5, layers = 2)
Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.