Deriving Unbounded Proof of Linear Hybrid Automata from Bounded Verification

摘要

The behavior space of real time hybrid systems is very complex and hence expensive to conduct the classical full state space model checking. Compared to the classical model checking, bounded model checking (BMC) is much cheaper to conduct and has better scalability. This work presents a technique that can derive, in some cases, a proof of unbounded reach ability argument of Linear Hybrid Automata (LHA) from a BMC procedure. During BMC of LHA, typical procedures can discover sets of unsatisfiable constraint cores, a.k.a. UC or IIS, in the constraint set according to the bounded continuous state space of LHA. Currently, such unsatisfiable constraints are only fed back to the constraint set to accelerate the BMC solving. In this paper, we propose that such unsatisfiable constraint core can be exploited to give general unbounded verification result of the system model. As each constraint can be mapped back to certain semantical elements of the system model, the unsatisfiable constraint cores can be mapped back into path segments, which are not feasible, in the graph structure of the LHA model. Clearly, if all the potential paths to reach the target location in the graph structure have to go through such infeasible path segments, the target location is not reachable in general, not only in the given bound. Based on this observation, we propose to encode the infeasible path segments as linear temporal logic (LTL) formulas, and present the graph structure, the discrete part, of the LHA model as a transition system. Then, we can take advantage of the mature off-the-shelf LTL model checking techniques to verify whether there exists a path to reach the target location without touching any detected IIS path segment in the graph structure of the LHA model. We implement this technique into a bounded LHA checker BACH. The experiments show that most of the benchmarks can be verified by the enhanced BACH with a clearly better performance and scalability.