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 [13] 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 [13]), the new approach proves not only insensitive to the hierarchical depth, but even leads to improved performance as the depth increases.

On Succinctness of Hierarchical State Diagrams in Absence of Message Passing

“…Note that our definition is different from generation of a single product machine. Our understanding of hierarchy, concurrency and flattening is rather similar to that of [1,3,12,6] and substantially different than that of [10,11]. Also note that trace inclusion is a rather strong conformance requirement for input-enabled deterministic systems.…”

Automated Verification of Executable UML Models

“…-Compositional exploration of state spaces [33,4]: The transition relation is split into several parts and only some of these are used in state space exploration. Selection of the employed parts is based on an analysis of the interaction between the parts and on the particular property one is interested in.…”

Modular refinement of hierarchic reactive machines

“…However, the notion of semantic equivalence used in all these papers is structural isomorphism of underlying state-transition graphs (or bisimilarity but with most of the structure visible), rather than conventional observational equivalences. Also there have been attempts to exploit the hierarchic states for efficient reachability analysis [Chan et al 1998;Alur and Yannakakis 1998;Behrmann et al 1999]. However, there is no observational semantics that allows defining a refinement preorder on hierarchic states.…”