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](./tutorial.md) 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](./examples/ex01.p6) as a Raku file.

The [Quine–McCluskey algorithm](https://en.wikipedia.org/wiki/Quine%E2%80%93McCluskey_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](./tutorial.md):

    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](https://github.com/int-main/Quine-McCluskey) implementing the algorithm and the paper [Programing implementation of the Quine-McCluskey method for minimization of Boolean expression](https://arxiv.org/abs/1410.1059).

AUTHOR
======

Luis F. Uceta 

LICENSE
=======

Artistic License 2.0