This paper defines an algorithm for predicting worst and best case execution times, and determining execution time constraints, of control-flow paths through real-time programs using their partial correctness semantics. The algorithm produces a linear approximation of path traversal conditions, worst and best case execution times and strongest postconditions for timed paths in abstract real-time programs. We further derive techniques to determine the set of control-flow paths with decidable worst and best case execution times. The approach is based on a weakest liberal precondition semantics and relies on supremum and infimum calculations similar to standard computations from Linear Programming and Presburger Arithmetic. The methodology is generic in that it is applicable to any executable language that can be supplied with a predicate transformer semantics and hence provides a verification basis for high level as well as assembler level execution time analysis techniques
