Application of majority voting and consensus voting algorithms in N-version software

N-version programming is one of the most common techniques which is used to improve the reliability of software by building in fault tolerance, redundancy and decreasing common cause failures. N different equivalent software versions are developed by N different and isolated workgroups by considering the same software specifications. The versions solve the same task and return results that have to be compared to determine the correct result. Decisions of N different versions are evaluated by a voting algorithm or the so-called voter. In this paper, two of the most commonly used software voting algorithms such as the majority voting algorithm and the consensus voting algorithm are studied. The distinctive features of N-version programming with majority voting and N-version programming with consensus voting are described. These two algorithms make a decision about the correct result on the base of the agreement matrix. However, if the equivalence relation on the agreement matrix is not satisfied it is impossible to make a decision. It is shown that the agreement matrix can be transformed into an appropriate form by using the Boolean compositions when the equivalence relation is satisfied.