A Logic-Based Approach to Model Checking of Parameterized and Infinite-State Systems

The aim of this thesis is to investigate the problem of verification for concurrent systems. In particular, a major problem in verification is that of validating systems, e.g. protocols, which are parametric, in the sense that the number of entities taking part in a given run is not fixed a priori. Typically, such kind of systems are also infinite-state, in that they use data structures containing possibly unbounded data values. In this thesis we tackle the problem of verification using a logical approach. In particular, the leading thread of this work will be a specification language based on a fragment of Girard’s linear logic, which we will show to have direct connections with classical formalisms like high-level nets or rewriting. By combining the power of logical connectives with the flexibility of rewriting, we are able to nicely model local and global transitions, and to elegantly express new data generation. Reasoning on heterogeneous domains can also be achieved via specialized constraint solvers. We show how this language can be used both for the specification and the analysis of parametric systems. In particular, we present a verification procedure which resembles classical symbolic model checking algorithms for infinite-state systems, and is well-suited to study system properties like safety, e.g. mutual exclusion. Technically, our verification procedure uses a fixpoint computation strategy which is based on a new bottom-up semantics for a fragment of linear logic. We illustrate our methodology presenting different examples coming from concurrency theory, like a parameterized version of the ticket mutual-exclusion protocol, and from security, like authentication protocols.