From Linear Temporal Logic Properties to Rewrite Propositions
Résumé
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. This approach has recently been studied using a non-automatic translation method. The extent to which such a translation can be systematised needs to be investigated, as well as the applicability of approximated methods wherever no exact translation can be effected. This paper presents contributions to that effect: 1) we investigate suitable semantics for LTL on maximal rewriting words and their influence on the feasibility of a translation, and 2) we propose a general scheme providing exact results on a fragment of LTL corresponding mainly to safety formulæ, and approximations on a larger fragment.