Bounded Model Checking of Max-Plus Linear Systems via Predicate Abstractions

Abstract

This paper introduces the abstraction of max-plus linear (MPL) systems via predicates. Predicates are automatically selected from system matrix, as well as from the specifications under consideration. We focus on verifying time-difference specifications, which encompass the relation between successive events in MPL systems. We implement a bounded model checking (BMC) procedure over a predicate abstraction of the given MPL system, to verify the satisfaction of time-difference specifications. Our predicate abstractions are experimentally shown to improve on existing MPL abstractions algorithms. Furthermore, with focus on the BMC algorithm, we can provide an explicit upper bound on the completeness threshold by means of the transient and the cyclicity of the underlying MPL system.

Computation of the Transient in Max-Plus Linear Systems via SMT-Solving

“…The computation of the transient is key to solve a number of fundamental problems of MPL systems, such as reachability analysis [22] and bounded model checking [23]: the transient plays a crucial role as the "completeness threshold" [11] for those two problems. The computation of the transient is an interesting problem, as it is not necessarily correlated to the dimension of the MPL system.…”