QCA (version 1.0-4)

findSupersets: Find Supersets of Configurations in the Implicant Matrix

Description

This function finds all possible unique supersets for a specific set of configurations in the implicant matrix.

Usage

findSupersets(noflevels3k, input.combs)

Arguments

noflevels3k

A vector containing the number of levels for each condition incremented by 1

input.combs

A matrix of configurations or a vector of their row numbers in the implicant matrix

Value

• A vector of the line numbers of all possible supersets in the implicant matrix

Details

The number of supersets for any combination of condition literals is equal to $2^k - 1$, where $k$ is the number of conditions. The implicant matrix consists of all configurations and their supersets, including the empty set. The formula for the number of implicants is $\prod_{j = 1}^{k}{p_j + 1}$, where $p_j$ is the number of levels for condition $j$ and $k$ is the number of conditions (Dusa, 2010, 2007). The findSupersets() function finds all unique supersets of a specific set of configurations in the implicant matrix.

References

A. Dusa. Enhancing Quine-McCluskey. WP 2007-49, COMPASSS, 2007. URL: http://www.compasss.org/wpseries/Dusa2007b.pdf.

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

See Also

getRow, findSubsets

Examples

# three conditions with two levels each
noflevels <- c(2, 2, 2)

# row number 14 of the implicant matrix corresponding to the configuration
# containing the first level of all condition
getRow(noflevels = noflevels + 1, row.no = 14) - 1

# the row numbers of the implicant matrix which correspond to supersets of this
# configuration
(rows <- findSupersets(noflevels + 1, input.combs = 14))

# the corresponding matrix representation of these rows 
getRow(noflevels = noflevels + 1, row.no = rows) - 1

# now for row numbers 14 and 17
getRow(noflevels = noflevels + 1, row.no = c(14, 17)) - 1
(rows <- findSupersets(noflevels + 1, input.combs = c(14, 17)))
getRow(noflevels = noflevels + 1, row.no = rows) - 1

# in matrix representation
(input.combs <- getRow(noflevels + 1, row.no = c(14, 17)))
findSupersets(noflevels + 1, input.combs = input.combs)