QCA (version 1.1-2)

demoChart: Create Prime Implicant Charts

Description

This function creates prime implicant charts. It is intended for demonstration purposes.

Usage

demoChart(primes = c(""), configs = c(""), prod.split = "")

Arguments

primes

A vector of prime implicants.

configs

A vector of configurations.

prod.split

The intersection (product) operator (if any).

Value

• A logical matrix whose elements indicate which prime implicants are supersets of which configurations.

Details

This function creates prime implicant (PI) charts as proposed by Quine (1952) and McCluskey (1956). PI charts have the prime implicants listed on the rows and the truth table configurations from which they have been derived listed on the columns. Each configuration must be covered at least once by at least one prime implicant. This function is intended for demonstration purposes only. When terms consist of more than simple letters, an intersection operator must be provided. For proper prime implicant chart analysis after minimization, use PIchart component returned by eqmcc().

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")
CO <- c("ABC", "Abc", "AbC", "aBc")
chart <- demoChart(PI, CO)
prettyTable(chart)

# 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)

# different intersection operators
PI <- c("AZ", "BY", "~CX")
CO <- c("AZ*BY*CX", "AZ*~BY*~CX", "AZ*~BY*CX", "~AZ*BY*~CX")
prettyTable(demoChart(PI, CO, prod.split = "*"))

CO <- gsub("*", "&", CO, fixed = TRUE)
prettyTable(demoChart(PI, CO, prod.split = "&"))