Incremental Generation of Linear Invariants for Component-Based Systems

Invariants generation has been intensively considered as an effective verification method for concurrent systems. However, none of the existing work on the topic strongly exploits the structure of the system and the algebra that defines the interactions between its components. This not only has an impact on the computation time, but also on the scalability of the method. In a series of recent work, we developed an efficient approach for generating invariants for systems described in the BIP component framework. BIP is an expressive modeling formalism including a rich algebra to describe component interactions. Our technique, which focuses on generating Boolean invariants corresponding to a subclass of the conjunctive normal form, was then extended to an incremental one capable of generating global invariants from smaller invariants obtained for sub-systems by exploiting the algebra that describes their interactions. This approach gives a panoply of techniques and libraries to rigurously design potentially complex systems. We also showed that Boolean invariants generated by our methodology correspond to trap of the Petri net induced by the BIP model. Unfortunately, this class of invariants may be too unprecise, and hence leads to discovery of false positive counter examples. The objective of this paper is to propose new techniques dedicated to the computation of linear interactions invariants, i.e., invariants that are described by linear constraints and that relate states of several components in the system. By definition, such new class is incomparable to the one of Boolean invariants, but we will show that it is generally more precise. In addition, we propose an incremental approach that allows to discover and reuse invariants that have already been computed on subparts of the model. Those new techniques have been implemented in DFINDER, a tool for checking deadlock freedom on BIP systems using invariants, and evaluated on several case studies. The experiments show that our approach outperforms classical techniques on a wide range of models.