Learning Assumptions for Compositional Verification

Abstract

Abstract. Compositional verification is a promising approach to addressing the state explosion problem associated with model checking. One compositional technique advocates proving properties of a system by checking properties of its components in an assume-guarantee style. However, the application of this technique is difficult because it involves non-trivial human input. This paper presents a novel framework for performing assume-guarantee reasoning in an incremental and fully automated fashion. To check a component against a property, our approach generates assumptions that the environment needs to satisfy for the property to hold. These assumptions are then discharged on the rest of the system. Assumptions are computed by a learning algorithm. They are initially approximate, but become gradually more precise by means of counterexamples obtained by model checking the component and its environment, alternately. This iterative process may at any stage conclude that the property is either true or false in the system. We have implemented our approach in the LTSA tool and applied it to a NASA system.

Automated Learning of Probabilistic Assumptions for Compositional Reasoning

“…To give a concrete example, we adopt the framework used in [15,32]. Components M i and assumption A are labelled transition systems and G is a safety property.…”

“…In particular, deciding how to break down a system into its components and devising suitable assumptions about the behaviour of those components initially proved difficult to automate. A breakthrough in this area came with the observation of [15] that learning techniques, such as Angluin's L* algorithm [3], could be used to automate the process of generating assumptions. In this section, we give a short description of L* and its application to automatic compositional verification of non-probabilistic systems.…”

“…In [15], it was shown how L* could be adapted to the problem of automatically generating assumptions for assumeguarantee verification of labelled transition systems. This is done by phrasing the problem in a language-theoretic setting: the assumption A to be generated is a labelled transition system, whose set of (finite) traces forms a regular language.…”

“…A variety of subsequent improvements and extensions to the basic technique of [15] were proposed (see e.g. [32] for details) and the approach was successfully applied to several large case studies.…”

“…When aiming to develop fully automated verification techniques, an important question that arises is how to devise suitable assumptions about system components. In the context of non-probabilistic systems, a breakthrough in the practical applicability of assume-guarantee verification came about through the adoption of algorithmic learning techniques to generate assumptions [15,32]. In recent work [20], we showed how learning could also be successfully used to generate the probabilistic assumptions needed for the compositional verification of probabilistic systems.…”