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

Parameterised verification of randomised distributed systems using state-based models

Model checking is a powerful technique for the verification of distributed systems but is limited to verifying systems with a fixed number of processes. The verification of a system for an arbitrary number of processes is known as the parameterised model checking problem and is, in general, undecidable. Parameterised model checking has been studied in depth for non-probabilistic distributed systems. We extend some of this work in order to tackle the parameterised model checking problem for distributed protocols that exhibit probabilistic behaviour, a problem that has not been widely addressed to date. In particular, we consider the application of network invariants and explicit induction to the parameterised verification of state-based models of randomised distributed systems. We demonstrate the use of network invariants by constructing invariant models for non-probabilistic and probabilistic forms of a simple counter token ring protocol. We show that proving properties of the invariants equates to proving properties of the token ring protocol for any number of processes. The use of induction is considered for the verification of a class of randomised distributed systems. These systems, termed degenerative, have the property that a model of a system with given communication graph eventually behaves like a model of a system with a reduced graph, where reduction is by removal of a set of nodes. We distinguish between deterministically, probabilistically and semi-degenerative systems, according to the manner in which a system degenerates. For the former two classes we describe induction schemas for reasoning about models of these systems over arbitrary communication graphs. We show that certain properties hold for models of such systems with any graph if they hold for all models of a system with some base graph and demonstrate this via case studies: two randomised leader election protocols. We illustrate how induction can also be employed to prove properties of semi-degenerative systems by considering a simple gossip protocol

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

Computer Aided Verification

This open access two-volume set LNCS 11561 and 11562 constitutes the refereed proceedings of the 31st International Conference on Computer Aided Verification, CAV 2019, held in New York City, USA, in July 2019. The 52 full papers presented together with 13 tool papers and 2 case studies, were carefully reviewed and selected from 258 submissions. The papers were organized in the following topical sections: Part I: automata and timed systems; security and hyperproperties; synthesis; model checking; cyber-physical systems and machine learning; probabilistic systems, runtime techniques; dynamical, hybrid, and reactive systems; Part II: logics, decision procedures; and solvers; numerical programs; verification; distributed systems and networks; verification and invariants; and concurrency