Parameterized Systems : Generalizing and Simplifying Automatic Verification

Rezine, A. 2008. Parameterized Systems: Generalizing and Simplifying Automatic Verification. Acta Universitatis Upsaliensis. Uppsala Dissertations from the Faculty of Science and Technology 72. 196 pp. Uppsala. ISBN 978-91-554-7138-5. In this thesis we propose general and simple methods for automatic verification of parameterized systems. These are systems consisting of an arbitrary number of identical processes or components. The number of processes defines the size of the system. A parameterized system may be regarded as an infinite family of instances, namely one for each size. The aim is to perform a parameterized verification, i.e. to verify that behaviors produced by all instances, regardless of their size, comply with some safety or liveness property. In this work, we describe three approaches to parameterized verification. First, we extend the Regular Model Checking framework to systems where components are organized in tree-like structures. For such systems, we give a methodology for computing the set of reachable configurations (used to verify safety properties) and the transitive closure (used to verify liveness properties). Next, we introduce a methodology allowing the verification of safety properties for a large class of parameterized systems. We focus on systems where components are organized in linear arrays and manipulate variables or arrays of variables ranging over bounded or numerical domains. We perform backwards reachability analysis on a uniform over-approximation of the parameterized system at hand. Finally, we suggest a new approach that enables us to reduce the verification of termination under weak fairness conditions to a reachability analysis for systems with simple commutativity properties. The idea is that reachability calculations (associated with safety) are usually less expensive then termination (associated with liveness). This idea can also be used for other transition systems and not only those induced by parameterized systems.