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It is shown that specifications of program performance can be formally verified. Formal verification techniques, in particular, the method of inductive assertions, can be adapted to show that a program's maximum or mean execution time is correctly described by specifications supplied with the program. To formally establish the mean execution time, branching probabilities are expressed using inductive assertions which involve probability distributions. Verification conditions are formed and proved which establish that if the input distribution is correctly described by the input specifications, then the inductive assertions correctly describe the probability distributions of the data during execution. Once the inductive assertions are shown to be correct, branching probabilities are obtained and mean computation time is computed.
Ben Wegbreit (1976) studied this question.