Quine McCluskey algorithm

What is that?

The Quine McCluskey algorithm is a method to minimize a boolean function into a canonical POS (product of sums) or SOP (sum of products) function.

I had a try with this algorithm for a specific need in a Vim plugin but it is too slow when there are too many different terms in the function.

Demo

$ vim qmc.vim
$ source %

INPUT -a b -c -d + a -b -c -d + a -b -c d + a -b c -d + a -b c d + a b -c -d + a b c -d + a b c d
TERMS ['a', 'b', 'c', 'd']
TRUTH TABLE
{'result': 0, 'mterm': ['0', '0', '0', '0']}
{'result': 0, 'mterm': ['0', '0', '0', '1']}
{'result': 0, 'mterm': ['0', '0', '1', '0']}
{'result': 0, 'mterm': ['0', '0', '1', '1']}
{'result': 1, 'mterm': ['0', '1', '0', '0']}
{'result': 0, 'mterm': ['0', '1', '0', '1']}
{'result': 0, 'mterm': ['0', '1', '1', '0']}
{'result': 0, 'mterm': ['0', '1', '1', '1']}
{'result': 1, 'mterm': ['1', '0', '0', '0']}
{'result': 1, 'mterm': ['1', '0', '0', '1']}
{'result': 1, 'mterm': ['1', '0', '1', '0']}
{'result': 1, 'mterm': ['1', '0', '1', '1']}
{'result': 1, 'mterm': ['1', '1', '0', '0']}
{'result': 0, 'mterm': ['1', '1', '0', '1']}
{'result': 1, 'mterm': ['1', '1', '1', '0']}
{'result': 1, 'mterm': ['1', '1', '1', '1']}
IMPLICANTS CHARTS
SIZE 1
{'prime': 0, 'terms': ['0', '1', '0', '0'], 'mterms': [4]}
{'prime': 0, 'terms': ['1', '0', '0', '0'], 'mterms': [8]}
{'prime': 0, 'terms': ['1', '0', '0', '1'], 'mterms': [9]}
{'prime': 0, 'terms': ['1', '0', '1', '0'], 'mterms': [10]}
{'prime': 0, 'terms': ['1', '0', '1', '1'], 'mterms': [11]}
{'prime': 0, 'terms': ['1', '1', '0', '0'], 'mterms': [12]}
{'prime': 0, 'terms': ['1', '1', '1', '0'], 'mterms': [14]}
{'prime': 0, 'terms': ['1', '1', '1', '1'], 'mterms': [15]}
SIZE 2
{'prime': 1, 'terms': ['-', '1', '0', '0'], 'mterms': [4, 12]}
{'prime': 0, 'terms': ['1', '0', '0', '-'], 'mterms': [8, 9]}
{'prime': 0, 'terms': ['1', '0', '-', '0'], 'mterms': [8, 10]}
{'prime': 0, 'terms': ['1', '-', '0', '0'], 'mterms': [8, 12]}
{'prime': 0, 'terms': ['1', '0', '-', '1'], 'mterms': [9, 11]}
{'prime': 0, 'terms': ['1', '0', '1', '-'], 'mterms': [10, 11]}
{'prime': 0, 'terms': ['1', '-', '1', '0'], 'mterms': [10, 14]}
{'prime': 0, 'terms': ['1', '-', '1', '1'], 'mterms': [11, 15]}
{'prime': 0, 'terms': ['1', '1', '-', '0'], 'mterms': [12, 14]}
{'prime': 0, 'terms': ['1', '1', '1', '-'], 'mterms': [14, 15]}
SIZE 4
{'prime': 1, 'terms': ['1', '0', '-', '-'], 'mterms': [8, 9, 10, 11]}
{'prime': 1, 'terms': ['1', '-', '-', '0'], 'mterms': [8, 10, 12, 14]}
{'prime': 1, 'terms': ['1', '-', '1', '-'], 'mterms': [10, 11, 14, 15]}
PRIME IMPLICANTS CHART
{'essential': 1, 'terms': ['-', '1', '0', '0'], 'mterms': [4, 12]}
{'essential': 1, 'terms': ['1', '0', '-', '-'], 'mterms': [8, 9, 10, 11]}
{'essential': 0, 'terms': ['1', '-', '-', '0'], 'mterms': [8, 10, 12, 14]}
{'essential': 1, 'terms': ['1', '-', '1', '-'], 'mterms': [10, 11, 14, 15]}
SOLUTION b -c -d + a -b + a c