The short-term objectives of this research are to design and evaluate general solutions to the problem of inexactness of values in fault-tolerant systems. The long-term goals are to understand the ways in which inherent redundancy in parallel and distributed systems can best be exploited to provide highly dependable multicomputing environments. Sources of inexactness include round-off error, noise, quantization error, diverse software, non-determinism, heterogeneity, and redundant sensors. Inexactness problems include approximate agreement, inexact agreement, clock synchronization, sensor fusion, diverse software, and inexact voting. In this project, new solution techniques for dealing with inexactness in parallel and distributed systems will be developed, and a unifying methodology for studying inexactness problems will be investigated. Techniques developed in the project will be evaluated analytically and in a network of workstations testbed. This research is expected to lead to more efficient and more powerful techniques for dealing with inexactness in fault-tolerant systems. The effect of these techniques will be increased precision of final results, lower communication overhead for redundancy, and increased overall system reliability.