The Improvement of Quine-McCluskey Method Using Set Covering Problem for Safety Systems

Abstract

When designing complex safety systems which consist of large scale logical circuits, the basic requirement is to minimise the number of elements that will implement the given logical functions. This will increase the reliability, and thus potentially the security of the devices. For logical functions with a number of variables of no more than 4, Karnaugh maps are preferred. However, in practice, we encounter much more complex functions, either directly applying Boolean algebra laws or using the Quine-McCluskey method, which is based on their systematic use. However, because this method does not provide a minimal form of logical function, and as a result, there may be redundant expressions, we will show that the additional phase of minimisation means solving the problem of covering all inputs by the obtained output expressions. For the purpose of clear representation and implementation process of post-processing method, the genetic algorithms and simulated annealing were implemented on OR-Library benchmarks.