**Commenced**in January 2007

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**Edition:**International

**Paper Count:**30517

##### Heuristic Set-Covering-Based Postprocessing for Improving the Quine-McCluskey Method

**Authors:**
Miloš Šeda

**Abstract:**

Finding the minimal logical functions has important applications in the design of logical circuits. This task is solved by many different methods but, frequently, they are not suitable for a computer implementation. We briefly summarise the well-known Quine-McCluskey method, which gives a unique procedure of computing and thus can be simply implemented, but, even for simple examples, does not guarantee an optimal solution. Since the Petrick extension of the Quine-McCluskey method does not give a generally usable method for finding an optimum for logical functions with a high number of values, we focus on interpretation of the result of the Quine-McCluskey method and show that it represents a set covering problem that, unfortunately, is an NP-hard combinatorial problem. Therefore it must be solved by heuristic or approximation methods. We propose an approach based on genetic algorithms and show suitable parameter settings.

**Keywords:**
Genetic Algorithm,
set covering problem,
Boolean algebra,
Karnaugh map,
Quine-McCluskey method

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1059733

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