Normalisation of Loops with Covariant Variables

Temporal property verification is utterly important to ensure safety of critical real-time systems. A main component of this verification is the computation of Worst Case Execution Time (WCET) that requires, in turn, the determination of loop bounds. Although a lot of efforts have been performed in this domain, it remains relatively common cases which are unsolved. For example, to our knowledge, no fast automatic method can cope with the loop bound of a simple binary search look-up. In this paper, we present an approach to solve such loops by using arithmetico-geometric series, that is, loops with arithmetic and/or geometric incrementation with several variables. We have implemented and experimented this approach in our tool oRange