Symbolic Techniques for Parametric Reasoning about Counter and Clock Systems

We address the problem of automatic analysis of parametric counter and clock automata. We propose a semi-algorithmic approach based on using (1) expressive symbolic representation structures called Parametric DBM's, and (2) accurate extrapolation techniques allowing to speed up the reachability analysis and help its termination. The techniques we propose consist in guessing automatically the eeect of iterating a control loop an arbitray number of times, and in checking that this guess is exact. Our approach can deal uniformly with systems that generate linear or nonlinear sets of conngurations. We have implemented our techniques and experimented them on nontrivial examples such as a parametric timed version of the Bounded Retransmission Protocol.