implicantMatrix {QCApro}

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.

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.

Value

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

Contributors

Dusa, Adrian	: programming
Thiem, Alrik	: development, documentation, testing

Author(s)

Alrik Thiem (Personal Website; ResearchGate Website)

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)