Quine-McCluskey logic function Simplification Algorithm (unfinished)

Quine-McCluskeyAlgorithmIs a logic function simplification method developed by W. v. Quine and Edward J. McCluskey, similar (Karnaugh Mapping) Simplification method, but this list-based algorithm is more suitable for computer language implementation, and provides a method to determine whether a function has reached the simplest degree. This method is also called tabulation simplification.

This method is calculated in two steps:

1. Find all the minimum items of the function (Prime implicants )

2. Find the minimum items contained in the function and other necessary minimum items in the minimum item table.

Complexity

Although it is more practical to process logic functions with four or more variables than the Kano diagram, the problem should be NP-hard. The Quine-McCluskey algorithm still has limitations in use. The algorithm running time increases exponentially with the number of variables. We can see that for a logical function with n variables, the minimum number of items can be 3 ^ n/n. If n = 32, there will be 6.5*10 ^ 15 minimum items. Therefore, logical functions that contain a large number of variables must be simplified using an unoptimized heuristic simplification method. Espresso heuristic logic minimizer is the de facto simplification standard.

Example