# NAME

QM - A Raku module that implements the Quine–McCluskey (QM) algorithm for simplifying Boolean functions

# DESCRIPTION

The **Quine-McCluskey** algorithm is a simplification technique to systematically reach a minimal solution using a system of any `n`

variables.

See the tutorial for more information about the algorithm which also has an example that walks through the algorithm. The same example can be found in examples/ex01.p6 as a Raku file.

The Quine–McCluskey algorithm on Wikipedia.

# INSTALLATION

### Using zef:

```
zef update && zef install QM
```

### From source:

```
git clone git@gitlab.com:uzluisf/quine-mccluskey.git
cd quine-mccluskey && zef install .
```

# SYNOPSIS

The module is implemented in a OO-style. To apply the algorithm, an object of the `QM`

must be instantiated through the `minterms`

. The following code snippet showcases all the methods made available by `QM`

using the example from the tutorial:

```
use QM;
my @regular-minterms = 0, 1, 2, 5, 6, 7, 8, 9, 10, 14;
my @dont-care = [];
# the don't care conditions array is optional.
my $qm = QM.minterms(@regular-minterms, @dont-care);
put $qm.all-minterms.join(', '); #=> 0, 1, 2, 5, 6, 7, 8, 9, 10, 14
put $qm.prime-implicants<all>; #=> 011- 0-01 01-1 --10 -00- -0-0
put $qm.essential-prime-implicants; #=> --10 -00-
put $qm.prime-implicants-chart.perl;
#=>
#`{
"0" => $["-00-", "-0-0"],
"1" => $["-00-", "0-01"],
"10" => $["--10", "-0-0"],
"14" => $["--10"],
"2" => $["--10", "-0-0"],
"5" => $["01-1", "0-01"],
"6" => $["--10", "011-"],
"7" => $["011-", "01-1"],
"8" => $["-00-", "-0-0"],
"9" => $["-00-"]
}
put $qm.prime-implicants-chart(:dec).perl;
#=>
# ([2, 6, 10, 14], [0, 2, 8, 10], [0, 1, 8, 9], [1, 5], [5, 7], [6, 7]).Seq
put $qm.reduced-boolean-expression; #=> A'BD + CD' + B'C'
```

# METHODS

`all-minterms`

- Return both the regular minterms and the don't care conditions if provided.`prime-implicants`

- Return all prime implicants for the boolean function, including the essential prime implicants.`essential-prime-implicants`

- Return the essential prime implicants for the boolean function.`prime-implicants-chart`

- Return a hash representing the Prime Implicant Chart (PIC) detailing the minterms and the prime implicants which cover them.`prime-implicants-chart(:dec)`

- Return a sequence of arrays of prime implicants as decimal numerals.

`reduced-boolean-expression`

- Return the minimal SoP for the boolean function.

# Materials

This modules was inspired by int-main's Python script implementing the algorithm and the paper Programing implementation of the Quine-McCluskey method for minimization of Boolean expression.

# AUTHOR

Luis F. Uceta

# LICENSE

Artistic License 2.0