Liveness Verification in TRSs Using Tree Automata and Termination Analysis

This paper considers verification of the liveness property Live(R, I, G) for a term rewrite system (TRS) R, where I (Initial states) and G (Good states) are two sets of ground terms represented by finite tree automata. Considering I and G, we transform R to a new TRS R' such that termination of R' proves the property Live(R, I, G)

Application of rewriting techniques to verification problems

The goal of the project is to employ techniques from term rewriting to verification problems. The relationship between liveness properties and termination of term rewrite systems (TRSs) is of particular interest. The emphasis is on the investigation of such properties for infinite state space systems where standard model checking techniques fail. Next to developing the necessary underlying theory and performing a case study analysis, the possibility to automate this approach is of great importance. In this paper we discuss the motivation of such work, present the results obtained so far, discuss related work and present plans for the further research

Regular Abstractions for Array Systems

Verifying safety and liveness over array systems is a highly challenging problem. Array systems naturally capture parameterized systems such as distributed protocols with an unbounded number of processes. Such distributed protocols often exploit process IDs during their computation, resulting in array systems whose element values range over an infinite domain. In this paper, we develop a novel framework for proving safety and liveness over array systems. The crux of the framework is to overapproximate an array system as a string rewriting system (i.e. over a finite alphabet) by means of a new predicate abstraction that exploits the so-called indexed predicates. This allows us to tap into powerful verification methods for string rewriting systems that have been heavily developed in the last few decades (e.g. regular model checking). We demonstrate how our method yields simple, automatically verifiable proofs of safety and liveness properties for challenging examples, including Dijkstra's self-stabilizing protocol and the Chang-Roberts leader election protocol

Predicate Diagrams as Basis for the Verification of Reactive Systems

This thesis proposes a diagram-based formalism for verifying temporal properties of reactive systems. Diagrams integrate deductive and algorithmic verification techniques for the verification of finite and infinite-state systems, thus combining the expressive power and flexibility of deduction with the automation provided by algorithmic methods. Our formal framework for the specification and verification of reactive systems includes the Generalized Temporal Logic of Actions (TLA*) from Merz for both mathematical modeling reactive systems and specifying temporal properties to be verified. As verification method we adopt a class of diagrams, the so-called predicate diagrams from Cansell et al. We show that the concept of predicate diagrams can be used to verify not only discrete systems, but also some more complex classes of reactive systems such as real-time systems and parameterized systems. We define two variants of predicate diagrams, namely timed predicate diagrams and parameterized predicate diagrams, which can be used to verify real-time and parameterized systems. We prove the completeness of predicate diagrams and study an approach for the generation of predicate diagrams. We develop prototype tools that can be used for supporting the generation of diagrams semi-automatically.In dieser Arbeit schlagen wir einen diagramm-basierten Formalismus für die Verifikation reaktiver Systeme vor. Diagramme integrieren die deduktiven und algorithmischen Techniken zur Verifikation endlicher und unendlicher Systeme, dadurch kombinieren sie die Ausdrucksstärke und die Flexibilität von Deduktion mit der von algoritmischen Methoden unterstützten Automatisierung. Unser Ansatz für Spezifikation und Verifikation reaktiver Systeme schließt die Generalized Temporal Logic of Actions (TLA*) von Merz ein, die für die mathematische Modellierung sowohl reaktiver Systeme als auch ihrer Eigenschaften benutzt wird. Als Methode zur Verifikation wenden wir Prädikaten-diagramme von Cansell et al. an. Wir zeigen, daß das Konzept von Prädikatendiagrammen verwendet werden kann, um nicht nur diskrete Systeme zu verifizieren, sondern auch kompliziertere Klassen von reaktiven Systemen wie Realzeitsysteme und parametrisierte Systeme. Wir definieren zwei Varianten von Prädikatendiagrammen, nämlich gezeitete Prädikatendiagramme und parametrisierte Prädikatendiagramme, die benutzt werden können, um die Realzeit- und parametrisierten Systeme zu verifizieren. Die Vollständigkeit der Prädikatendiagramme wird nachgewiesen und ein Ansatz für die Generierung von Prädikatendiagrammen wird studiert. Wir entwickeln prototypische Werkzeuge, die die semi-automatische Generierung von Diagrammen unterstützen

Read Operators and their Expressiveness in Process Algebras

We study two different ways to enhance PAFAS, a process algebra for modelling asynchronous timed concurrent systems, with non-blocking reading actions. We first add reading in the form of a read-action prefix operator. This operator is very flexible, but its somewhat complex semantics requires two types of transition relations. We also present a read-set prefix operator with a simpler semantics, but with syntactic restrictions. We discuss the expressiveness of read prefixes; in particular, we compare them to read-arcs in Petri nets and justify the simple semantics of the second variant by showing that its processes can be translated into processes of the first with timed-bisimilar behaviour. It is still an open problem whether the first algebra is more expressive than the second; we give a number of laws that are interesting in their own right, and can help to find a backward translation.Comment: In Proceedings EXPRESS 2011, arXiv:1108.407

Analysing Mutual Exclusion using Process Algebra with Signals

In contrast to common belief, the Calculus of Communicating Systems (CCS) and similar process algebras lack the expressive power to accurately capture mutual exclusion protocols without enriching the language with fairness assumptions. Adding a fairness assumption to implement a mutual exclusion protocol seems counter-intuitive. We employ a signalling operator, which can be combined with CCS, or other process calculi, and show that this minimal extension is expressive enough to model mutual exclusion: we confirm the correctness of Peterson's mutual exclusion algorithm for two processes, as well as Lamport's bakery algorithm, under reasonable assumptions on the underlying memory model. The correctness of Peterson's algorithm for more than two processes requires stronger, less realistic assumptions on the underlying memory model.Comment: In Proceedings EXPRESS/SOS 2017, arXiv:1709.0004