Assume-Guarantee Verification for Probabilistic Systems

Abstract

Abstract. We present a compositional verification technique for systems that exhibit both probabilistic and nondeterministic behaviour. We adopt an assume-guarantee approach to verification, where both the assumptions made about system components and the guarantees that they provide are regular safety properties, represented by finite automata. Unlike previous proposals for assume-guarantee reasoning about probabilistic systems, our approach does not require that components interact in a fully synchronous fashion. In addition, the compositional verification method is efficient and fully automated, based on a reduction to the problem of multi-objective probabilistic model checking. We present asymmetric and circular assume-guarantee rules, and show how they can be adapted to form quantitative queries, yielding lower and upper bounds on the actual probabilities that a property is satisfied. Our techniques have been implemented and applied to several large case studies, including instances where conventional probabilistic verification is infeasible.

Automated Learning of Probabilistic Assumptions for Compositional Reasoning

“…Prior to this, it is often necessary to construct a product PA for analysis. For example, for the probabilistic safety properties described above, we would construct the synchronous product of the PA to be verified and the DFA representing the safety property [29]. Tool support for verifying PAs (or MDPs) is also available: several probabilistic model checkers have been developed and are widely used.…”

“…Example 1. In Figure 1, we show a simple example (taken from [29]) comprising two components, each modelled as a PA. Component M 1 represents a controller that powers down devices.…”

“…1. Example, from [29]: two PAs M1, M2 and the DFA G err for a safety property G; we have that M1 M2 satisfies probabilistic safety property G 0.98 .…”

“…In this paper, we focus on the probabilistic assume-guarantee framework of [29]. This makes no restrictions on the PAs that can be analysed, nor the way that they are composed in parallel; instead it opts to use a less expressive form for assumptions, namely probabilistic safety properties.…”

“…In this paper, we discuss some recent developments in the area of automated compositional verification techniques for probabilistic systems, focusing on assume-guarantee verification techniques [29,21] for probabilistic automata [35,36], a natural model for compositional reasoning. When aiming to develop fully automated verification techniques, an important question that arises is how to devise suitable assumptions about system components.…”