findSubsets: Find all possible subsets of a given prime implicant

Description

It is a general rule that all subsets 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). If a prime implicant can be considered a superset of an initial combination of causal conditions, the reverse is also true: the initial combination is a subset of a prime implicant. Even more, a less minimum prime implicant (with more literals) is also a subset of another shorter (more minimum) prime implicant. This function finds all possible such subsets for a given prime implicant, in the $n^k$ space.

Usage

findSubsets(noflevels, row.no, maximum)

Arguments

noflevels

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

row.no

the row number where the (minimum) prime implicant is located

maximum

the maximum line number (subset) to be returned

Value

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

References

Dusa, Adrian (2010) A mathematical approach to the boolean minimization problem, Quality & Quantity vol.44, no.1, pp.99-113

Dusa, Adrian (2007) Enhancing Quine-McCluskey, http://www.compasss.org/files/WPfiles/Dusa2007a.pdf

Examples

Run this code

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

findSubsets(noflevels + 1, 2)     #  5  8 11 14 17 20 23 26

# stopping at maximum row number 20
findSubsets(noflevels + 1, 2, 20) #  5  8 11 14 17 20