Liveness of Randomised Parameterised Systems under Arbitrary Schedulers (Technical Report)

We consider the problem of verifying liveness for systems with a finite, but unbounded, number of processes, commonly known as parameterised systems. Typical examples of such systems include distributed protocols (e.g. for the dining philosopher problem). Unlike the case of verifying safety, proving liveness is still considered extremely challenging, especially in the presence of randomness in the system. In this paper we consider liveness under arbitrary (including unfair) schedulers, which is often considered a desirable property in the literature of self-stabilising systems. We introduce an automatic method of proving liveness for randomised parameterised systems under arbitrary schedulers. Viewing liveness as a two-player reachability game (between Scheduler and Process), our method is a CEGAR approach that synthesises a progress relation for Process that can be symbolically represented as a finite-state automaton. The method is incremental and exploits both Angluin-style L*-learning and SAT-solvers. Our experiments show that our algorithm is able to prove liveness automatically for well-known randomised distributed protocols, including Lehmann-Rabin Randomised Dining Philosopher Protocol and randomised self-stabilising protocols (such as the Israeli-Jalfon Protocol). To the best of our knowledge, this is the first fully-automatic method that can prove liveness for randomised protocols.Comment: Full version of CAV'16 pape

Learning to Prove Safety over Parameterised Concurrent Systems (Full Version)

We revisit the classic problem of proving safety over parameterised concurrent systems, i.e., an infinite family of finite-state concurrent systems that are represented by some finite (symbolic) means. An example of such an infinite family is a dining philosopher protocol with any number n of processes (n being the parameter that defines the infinite family). Regular model checking is a well-known generic framework for modelling parameterised concurrent systems, where an infinite set of configurations (resp. transitions) is represented by a regular set (resp. regular transducer). Although verifying safety properties in the regular model checking framework is undecidable in general, many sophisticated semi-algorithms have been developed in the past fifteen years that can successfully prove safety in many practical instances. In this paper, we propose a simple solution to synthesise regular inductive invariants that makes use of Angluin's classic L* algorithm (and its variants). We provide a termination guarantee when the set of configurations reachable from a given set of initial configurations is regular. We have tested L* algorithm on standard (as well as new) examples in regular model checking including the dining philosopher protocol, the dining cryptographer protocol, and several mutual exclusion protocols (e.g. Bakery, Burns, Szymanski, and German). Our experiments show that, despite the simplicity of our solution, it can perform at least as well as existing semi-algorithms.Comment: Full version of FMCAD'17 pape

A generic approach for the automatic verification of featured, parameterised systems

A general technique is presented that allows property based feature analysis of systems consisting of an arbitrary number of components. Each component may have an arbitrary set of safe features. The components are defined in a guarded command form and the technique combines model checking and abstraction. Features must fulfill certain criteria in order to be safe, the criteria express constraints on the variables which occur in feature guards. The main result is a generalisation theorem which we apply to a well known example: the ubiquitous, featured telephone system

Automatic verification of any number of concurrent, communicating processes

The automatic verification of concurrent systems by model-checking is limited due to the inability to generalise results to systems consisting of any number of processes. We use abstraction to prove general results, by model-checking, about feature interaction analysis of a telecommunications service involving any number of processes. The key idea is to model-check a system of constant number (m) of concurrent processes, in parallel with an "abstract" process which represents the product of any number of other processes. The system, for any specified set of selected features, is generated automatically using Perl scripts

Model Checking - My 27-Year Quest to Overcome the State Explosion Problem

Model Checking is an automatic verification technique for state-transition systems that are finite=state or that have finite-state abstractions. In the early 1980 s in a series of joint papers with my graduate students E.A. Emerson and A.P. Sistla, we proposed that Model Checking could be used for verifying concurrent systems and gave algorithms for this purpose. At roughly the same time, Joseph Sifakis and his student J.P. Queille at the University of Grenoble independently developed a similar technique. Model Checking has been used successfully to reason about computer hardware and communication protocols and is beginning to be used for verifying computer software. Specifications are written in temporal logic, which is particularly valuable for expressing concurrency properties. An intelligent, exhaustive search is used to determine if the specification is true or not. If the specification is not true, the Model Checker will produce a counterexample execution trace that shows why the specification does not hold. This feature is extremely useful for finding obscure errors in complex systems. The main disadvantage of Model Checking is the state-explosion problem, which can occur if the system under verification has many processes or complex data structures. Although the state-explosion problem is inevitable in worst case, over the past 27 years considerable progress has been made on the problem for certain classes of state-transition systems that occur often in practice. In this talk, I will describe what Model Checking is, how it works, and the main techniques that have been developed for combating the state explosion problem