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Modular and Incremental Analysis of Concurrent Software Systems
 by Dr. Hassen Sa´di.

Abstract
Modularization and abstraction are the keys to practical verification and analysis of large and complex systems. We present in an incremental methodology for the automatic analysis and verification of concurrent software systems. Our methodology is based on the theory of abstract interpretation. We first propose a compositional dataflow analysis algorithm that computes invariants of concurrent systems by composing invariants generated separately for each component. We present a novel compositional rule allow ing us to obtain invariants of the whole system as conjunctions of local invariants of each component. We also show how the generated invariants are used to construct, almost for free, finite state abstractions of the original system that preserve safety properties. This reduces dramatically the cost of computing such abstractions as reported in previous work. We finally give a novel refinement algorithm that re fines the constructed abstraction until the property of interest is proved or a counterexample is exhibited. Our methodology is implemented in a framework that combines deductive methods supported by theorem proving techniques and algorithmic methods supported by model checking and abstract interpretation techniques.
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