Model Checking a Temporal Logic via Program Verification

The thesis explores the possibility of viewing Model Checking as an instance of program verification in order to allow for the reuse of the vast theory and toolset of Abstract Interpretation in the setting of Model Checking. Model Checking is a formal verification technique used to analyse the correctness of software systems, based on a representation of the system as a formal model, such as a finite-state machine or a transition system, and on a representation of the properties it must satisfy as temporal logic formulae. On the other hand, Abstract Interpretation is a program analysis method, based on the idea of extracting properties of programs by (over-)approximating their semantics over a so-called abstract domain, typically a complete lattice, whose elements represent program properties. The thesis focuses on ACTL, the universal fragment of the temporal logic CTL, which can describe properties of executions which are universally quantified. It shows how properties expressed in ACTL can be mapped into programs written in a suitable programming language, whose semantics consists of counterexamples to the validity of the formula. Then such a program is analysed by Abstract Interpretation over some abstract domain, exploiting the idea of local completeness as put forward in some recent work, combining lower- and under-approximations.