QCA (version 1.1-2)

findSupersets: Find all Supersets of an Implicant

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 (values) for each variable 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 of an implicant in the implicant matrix.

Details

All supersets of an implicant can be found in the implicant matrix. An implicant matrix consists of all truth table configurations and their supersets, including the empty set (Dusa 2007, 2010). The total number of implicants $q$ is given by $q = \prod_{j = 1}^{k}{(p_{j} + 1)}$, where $p_{j}$ is the number of values for condition variable $j$ and $k$ is the total number of condition variables. The function findSupersets() finds all row numbers in the implicant matrix that correspond to all possible supersets of an implicant.

References

Dusa, Adrian. 2007. Enhancing Quine-McCluskey. COMPASSS: WP 2007-49. Available from: http://www.compasss.org/wpseries/Dusa2007b.pdf. Dusa, Adrian. 2010. A Mathematical Approach to the Boolean Minimization Problem. Quality & Quantity 44 (1):99-113.

See Also

findSubsets, getRow

Examples

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

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

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

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

# now for rows 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)