Section: New Results

Model-based Verification

We have investigated extensions of regular model-checking to new classes of rewrite relations on trees. We have studied specification and proof of modular imperative programs.

In the regular model-checking framework, reachability analysis can be guided by temporal logic properties, for instance to achieve the counter example guided abstraction refinement (CEGAR) objectives. A way to perform this analysis is to translate a temporal logic formula expressed on maximal rewriting words into a “rewrite proposition” – a propositional formula whose atoms are language comparisons, and then to generate semi-decision procedures based on (approximations of) the rewrite proposition. In [13] we have investigated suitable semantics for LTL on maximal rewriting words and their influence on the feasibility of a translation, and we have proposed a general scheme providing exact results for a fragment of LTL corresponding mainly to safety formulæ, and approximations for a larger fragment.

We address the following general problem of regular model-checking: decide whether $R^{*}\left(L\right)\cap L_p=\varnothing$ where $R^{*}$ is the reflexive and transitive closure of a successor relation $R$, and $L$ and $L_p$ are both regular tree languages. Considering a relation $R$ on finite words and a regular language $L$ encoding the initial configurations of a system, the set $R^{*}\left(L\right)$ of accessible words is not necessarily regular. Therefore, a way to verify safety properties is to over-approximate the set of reachable words by a regular language. In [42] , we develop new efficient approximation techniques based on syntactic criteria. When these syntactic over-approximations are too coarse, we propose CEGAR-like techniques to refine them using counter-examples. The approach has been successfully applied to verify mutual exclusion protocols.