The consistent comparison problem in N-version software

Abstract

The authors have identified a difficulty in the implementation of N-version programming. The problem, called the consistent comparison problem, arises for applications in which decisions are based on the results of comparing finite-precision numbers. It is shown that when versions make comparisons involving the results of finite-precision calculations, it is impossible to guarantee the consistency of their results. It is therefore possible that correct versions may arrive at completely different outputs for an application that does not apparently have multiple correct solutions. If this problem is not dealt with explicitly, an N-version system may be unable to reach consensus even when none of its component versions falls.