QCApro (version 1.1-1)

implicantMatrix: Create Implicant Matrices

Description

This function creates implicant matrices. An implicant matrix consists of all truth table minterms and their subsets, including the empty set.

Usage

implicantMatrix(noflevels, raw = FALSE, arrange = FALSE)

Arguments

noflevels

The number of levels for each exogenous factor.

raw

Logical, return implicant matrix with indicator for elimination.

arrange

Logical, arrange for easier visual inspection.

Value

A matrix with $\prod_{j = 1}^{k}{(p_{j} + 1)}$ rows and $k$ columns.

Contributors

Dusa, Adrian

: programming

Details

An implicant matrix consists of all minterms and their subsets, including the empty set (Dusa 2007, 2010; Thiem and Dusa 2015). The number of implicants $q$ is given by $q = \prod_{j = 1}^{k}{(p_{j} + 1)}$, where $p_{j}$ is the number of levels for factor $j$ and $k$ is the total number of exogenous factors.

If raw = TRUE, the indicator for elimination (-1) is used.

References

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

Dusa, Adrian. 2010. “A Mathematical Approach to the Boolean Minimization Problem.” Quality & Quantity 44 (1):99-113. DOI: 10.1007/s11135-008-9183-x.

Dusa, Adrian, and Alrik Thiem. 2015. “Enhancing the Minimization of Boolean and Multivalue Output Functions with eQMC.” Journal of Mathematical Sociology 39 (2):92-108. DOI: 10.1080/0022250X.2014.897949.

See Also

mintermMatrix

Examples

# three exogenous factors with two levels each;
# first row is empty set
implicantMatrix(noflevels = rep(2, 3))

# two exogenous factors with three levels each
implicantMatrix(noflevels = rep(3, 2))

# arranged differently
implicantMatrix(noflevels = rep(3, 2), arrange = TRUE)

# with internal indicator for eliminated values
implicantMatrix(noflevels = rep(3, 2), raw = TRUE)