A Transformational Approach for Generating Non-Linear Invariants

Saddek Bensalem (1) , Marius Bozga (1) , Jean-Claude Fernandez (2) , Constantin Lucian Ghirvu (1) , Yassine Lakhnech (1)

1 VERIMAG - IMAG - VERIMAG
2 LSR - IMAG - Laboratoire Logiciels Systèmes Réseaux

Computing invariants is the key issue in the analysis of infinite-state systems whether analysis means testing, verification or parameter synthesis. In particular, methods that allow to treat combinations of loops are of interest. We present a set of algorithms and methods that can be applied to characterize over-approximations of the set of reachable states of combinations of self-loops. We present two families of complementary techniques. The first one identifies a number of basic cases of pair of self-loops for which we provide an exact characterization of the reachable states. The second family of techniques is a set of rules based on static analysis that allow to reduce $n$ self-loops ($n\geq 2$) to $n-1$ independent pairs of self-loops. The results of the analysis of the pairs of self-loops can then be combined to provide an over-approximation of the reachable states of the $n$ self-loops. We illustrate our methods by synthesizing conditions under which the Biphase Mark protocol works properly.

Keywords: invariant generation; acceleration; protocol verification; Presburger arithmetic

Domains: Embedded Systems

Saddek Bensalem, Marius Bozga, Jean-Claude Fernandez, Constantin Lucian Ghirvu, Yassine Lakhnech. A Transformational Approach for Generating Non-Linear Invariants. Static Analysis 7th International Symposium, SAS 2000, Jun 2000, Santa Barbara, CA, United States. pp.58-72, ⟨10.1007/b87738⟩. ⟨hal-00369355⟩