The Consistent Comparison Problem in N-Version Software

We have identified a difficulty in the implementation of N-version programming. The problem, which we call the Consistent Comparison Problem, arises for applications in which decisions are based on the results of comparisons of finite-precision numbers. We show 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 a consensus even when none of its component versions fails.