Maximum likelihood voting for fault-tolerant software with finite output-space

When the output space of a multiversion software is finite, several software versions can give identical but incorrect outputs. This paper proposes a maximum likelihood voting (MLV) strategy for multiversion software with finite output-space under the assumption of failure independence. To estimate the correct result, MLV uses the reliability of each software version and determines the most likely correct result. In addition, two enhancements are made to MLV: (1) imposition of a requirement α* that the most likely correct output must have probability of at least α*; and (2) the voter can estimate when it has received one or more outputs from the software versions. If the probability that the estimated result is correct and is at least α*, then it immediately gives this estimated output. Since the voter need not wait for all the outputs before it can estimate, the required mean execution time can be reduced. The numerical results show that these MLV strategies have better performance than consensus voting and majority voting, especially when the variation of software version reliability is large. Enhancement #2 can appreciably reduce the mean execution time, especially when the software versions have larger execution time standard-deviation