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The tolerance theory by Arora and Kulkarni views a fault-tolerant program as the composition of a fault-intolerant program and fault tolerance components called detectors and correctors.At its core, the theory assumes that the correctness specifications under consideration are fusion closed.In general, fusion closure of specifications can be achieved by adding history variables to the program. However, addition of history variables causes an exponential growth of the state space of the program.To redress this problem, we present a method which can be used to add history information to a program in a way that (in a certain sense) minimizes the additional states. Hence, automated methods that add fault tolerance can now be efficiently applied to environments with not fusion closed specifications.