Verification of Hierarchical State/Event Systems using Reusability and Compositionality

Abstract

We investigate techniques for verifying hierarchical systems, i.e., finite state systems with a nesting capability. The straightforward way of analysing a hierarchical system is to first flatten it into an equivalent non-hierarchical system and then apply existing finite state system verification techniques. Though conceptually simple, flattening is severely punished by the hierarchical depth of a system. To alleviate this problem, we develop a technique that exploits the hierarchical structure to reuse earlier reachability checks of superstates to conclude reachability of substates. We combine the reusability technique with the successful compositional technique of J. Lind-Nielsen, H.R. Andersen, G. Behrmann, H. Hulgaard, K. Kristoffersen, and K.G. Larsen, 1998. In: Tools and Algorithms for the Construction and Analysis of Systems, Vol. 1384 of Lecture Notes in Computer Science, pp. 201–216, and investigate the combination experimentally on industrial systems and hierarchical systems generated according to our expectations to real systems. The experimental results are very encouraging: whereas a flattening approach degrades in performance with an increase in the hierarchical depth (even when applying the technique of J. Lind-Nielsen et al. (1998)), the new approach proves not only insensitive to the hierarchical depth, but even leads to improved performance as the depth increases.