Replication and Abstraction: Symmetry in Automated Formal Verification.

This article surveys fundamental and applied aspects of symmetry in system models, and of symmetry reduction methods used to counter state explosion in model checking, an automated formal verification technique. While covering the research field broadly, we particularly emphasize recent progress in applying the technique to realistic systems, including tools that promise to elevate the scope of symmetry reduction to large-scale program verification. The article targets researchers and engineers interested in formal verification of concurrent systems

Probabilistic symmetry reduction

Model checking is a technique used for the formal verification of concurrent systems. A major hindrance to model checking is the so-called state space explosion problem where the number of states in a model grows exponentially as variables are added. This means even trivial systems can require millions of states to define and are often too large to feasibly verify. Fortunately, models often exhibit underlying replication which can be exploited to aid in verification. Exploiting this replication is known as symmetry reduction and has yielded considerable success in non probabilistic verification. The main contribution of this thesis is to show how symmetry reduction techniques can be applied to explicit state probabilistic model checking. In probabilistic model checking the need for such techniques is particularly acute since it requires not only an exhaustive state-space exploration, but also a numerical solution phase to compute probabilities or other quantitative values. The approach we take enables the automated detection of arbitrary data and component symmetries from a probabilistic specification. We define new techniques to exploit the identified symmetry and provide efficient generation of the quotient model. We prove the correctness of our approach, and demonstrate its viability by implementing a tool to apply symmetry reduction to an explicit state model checker

Automatic techniques for detecting and exploiting symmetry in model checking

The application of model checking is limited due to the state-space explosion problem – as the number of components represented by a model increase, the worst case size of the associated state-space grows exponentially. Current techniques can handle limited kinds of symmetry, e.g. full symmetry between identical components in a concurrent system. They avoid the problem of automatic symmetry detection by requiring the user to specify the presence of symmetry in a model (explicitly, or by annotating the associated specification using additional language keywords), or by restricting the input language of a model checker so that only symmetric systems can be specified. Additionally, computing unique representatives for each symmetric equivalence class is easy for these limited kinds of symmetry. We present a theoretical framework for symmetry reduction which can be applied to explicit state model checking. The framework includes techniques for automatic symmetry detection using computational group theory, which can be applied with no additional user input. These techniques detect structural symmetries induced by the topology of a concurrent system, so our framework includes exact and approximate techniques to efficiently exploit arbitrary symmetry groups which may arise in this way. These techniques are also based on computational group theoretic methods. We prove that our framework is logically sound, and demonstrate its general applicability to explicit state model checking. By providing a new symmetry reduction package for the SPIN model checker, we show that our framework can be feasibly implemented as part of a system which is widely used in both industry and academia. Through a study of SPIN users, we assess the usability of our automatic symmetry detection techniques in practice