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A mathematical approach to the boolean minimization problem

Abstract

Any minimization problem involves a computer algorithm. Many such algorithms have been developed for the boolean minimizations, in diverse areas from computer science to social sciences (with the famous QCA algorithm). For a small number of entries (causal conditions in the QCA) any such algorithm will find a minimal solution, especially with the aid of the modern computers. However, for a large number of conditions a quick and complete solution is not easy to find using an algorithmic approach, due to the extremely large space of possible combinations to search in. In this article I will demonstrate a simple alternative solution, a mathematical method to obtain all possible minimized prime implicants. This method is not only easier to understand than other complex algorithms, but it proves to be a faster method to obtain an exact and complete boolean solution.

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Correspondence to Adrian Duşa.

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Duşa, A. A mathematical approach to the boolean minimization problem. Qual Quant 44, 99 (2010). https://doi.org/10.1007/s11135-008-9183-x

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Keywords

  • Qualitative comparative analysis
  • Boolean minimization
  • Computer algorithms
  • Small-N research