findSupersets: Find all Possible Supersets of One or Several Combinations

Description

It is a general rule that all supersets can be found in the $n^k$ space, understood as all possible combinations of values in any combination of bases $n$, each causal condition having three or more levels (Dusa, 2010, 2007). There is a finite number of prime implicants for any combination of causal conditions, equal to $2^k - 1$, where $k$ is the number of causal conditions. Counting out the input combination itself, the actual number is $2^k - 2$. This function computes all possible unique supersets for a specific set of combinations (either to explain or to exclude).

Usage

findSupersets(noflevels, input.combs)

Arguments

noflevels

A vector containing the number of levels for each causal condition plus 1 (because all prime implicants are to be found in the higher matrix)

input.combs

A matrix with combinations of causal conditions or a vector of line numbers from the same matrix

Value

a vector with the line numbers of all possible prime implicants in the $3^k$ space

References

A. Dusa. Enhancing Quine-McCluskey. WP 2007-49, COMPASSS, 2007. URL: http://www.compasss.org/files/WPfiles/Dusa2007a.pdf.

A. Dusa. A Mathematical Approach to the Boolean Minimization Problem. Quality & Quantity, 44(1): 99-113, 2010.

Examples

Run this code

# all three conditions are binary, having two levels: 0 and 1
noflevels <- c(2, 2, 2)

# 2 4 5 10 11 13 14
findSupersets(noflevels + 1, 14)

# 2 7 8 10 11 16 17
findSupersets(noflevels + 1, 17)

# both line numbers 14 and 17
# 2 4 5 7 8 10 11 13 14 16 17
findSupersets(noflevels + 1, c(14, 17))


# input.combs as a matrix
(input.combs <- getRow(noflevels + 1, c(14, 17)))

#     [,1] [,2] [,3]
#[1,]    1    1    1
#[2,]    1    2    1

# 2 4 5 7 8 10 11 13 14 16 17
findSupersets(noflevels + 1, input.combs)