Abstract

Hybrid systems represent an important and powerful formalism for modeling real-world applications such as embedded systems. A verification tool like SpaceEx is based on the exploration of a symbolic search space (the region space). As a verification tool, it is typically optimized towards proving the absence of errors. In some settings, e.g., when the verification tool is employed in a feedback-directed design cycle, one would like to have the option to call a version that is optimized towards finding an error trajectory in the region space. A recent approach in this direction is based on guided search. Guided search relies on a cost function that indicates which states are promising to be explored, and preferably explores more promising states first. In this paper, we propose an abstraction-based cost function based on coarse-grained space abstractions for guiding the reachability analysis. For this purpose, a suitable abstraction technique that exploits the flexible granularity of modern reachability analysis algorithms is introduced. The new cost function is an effective extension of pattern database approaches that have been successfully applied in other areas. The approach has been implemented in the SpaceEx model checker. The evaluation shows its practical potential.

Highlights

  • Hybrid systems are extended finite automata whose discrete states correspond to the various modes of continuous dynamics a system may exhibit, and whose transitions express the switching logic between these modes [1]

  • We introduce an abstraction-based cost function for hybrid systems which is motivated by pattern databases (PDBs)

  • We have explored the application of coarse-grained space abstractions to compute PDBs for hybrid systems

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Summary

Introduction

Hybrid systems are extended finite automata whose discrete states correspond to the various modes of continuous dynamics a system may exhibit, and whose transitions express the switching logic between these modes [1]. Hybrid systems have been used to model and to analyze various types of embedded systems [5,9,19,20,34,35,41]. A hybrid system is considered safe if a given set of bad states cannot be reached from the initial states. Reachability analysis is a main concern for hybrid systems. Since the reachability analysis of hybrid systems is in general undecidable [1], modern reachability analysis tools such as SpaceEx [23] resort to semi-decision procedures based on over-approximation techniques [16,23]. We explore the utility of guided search in order to improve the efficiency of such techniques

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