QCA (version 1.1-3)

solveChart: Eliminate Redundant Prime Implicants

Description

This function reduces the complete union of prime implicants to a minimal union by eliminating redundant prime implicants.

Usage

solveChart(chart, row.dom = FALSE, min.dis = TRUE, ...)

Arguments

chart

A prime implicant chart.

row.dom

Logical, impose row dominance as constraint on solution to eliminate dominated inessential prime implicants.

min.dis

Logical, impose minimal disjunctivity as constraint on solution to eliminate models with more prime implicants than the model(s) with the fewest prime implicants.

...

Other arguments (for backward compatibility).

Value

• A matrix containing in its columns the row index values from the prime implicant chart that form solutions according to the values specified by the user in the function's arguments.

Details

This function solves prime implicant charts. Prime implicant charts have the prime implicants listed on the rows and the truth table configurations from which they have been derived listed on the columns (Quine 1952; McCluskey 1956). Each configuration must be covered at least once by at least one prime implicant.

References

McCluskey, Edward J. 1956. Minimization of Boolean Functions. Bell Systems Technical Journal 35 (6):1417-44. Quine, Willard V. 1952. The Problem of Simplifying Truth Functions. American Mathematical Monthly 59 (8):521-31.

Examples

# simple PI chart, formatted using internal function prettyTable()
PI <- c("A", "B", "c", "D") 
CO <- c("AbCD", "AbCd", "aBcd", "aBCD") 
chart <- demoChart(PI, CO)
prettyTable(chart)

# solution:
# first or third PI: A + c
solveChart(chart)

# all non-overlapping solutions: 
# first or third PI: A + c
# second or third or fourth PI: B + c + D
solveChart(chart, min.dis = TRUE)

# a more complex example
PI <- c("AB", "BC", "Ac", "aC", "abd", "bcd")
CO <- c("ABCD", "ABCd", "ABcD", "ABcd", "AbcD", "Abcd",
        "aBCD", "aBCd", "abCD", "abCd", "abcd")
chart <- demoChart(PI, CO)
prettyTable(chart)

# AB + Ac + aC + abd
# AB + Ac + aC + bcd
# BC + Ac + aC + abd
# BC + Ac + aC + bcd
solveChart(chart)