On first-order runtime enforcement of branching-time properties

Runtime enforcement is a dynamic analysis technique that uses monitors to enforce the behaviour specified by some correctness property on an executing system. The enforceability of a logic captures the extent to which the properties expressible via the logic can be enforced at runtime for a specified operational model of enforcing monitors. We study the enforceability of branching-time, first-order properties expressed in the Hennessy-Milner Logic with Recursion (mu HML) with respect to monitors that can enforce behaviour involving events that carry data. To this end, we develop an operational framework for first-order enforcement via suppressions, insertions and replacements. We then use this model to formalise the meaning of enforcing a branching-time property. We also show that a safety syntactic fragment of the logic is enforceable within this framework by providing an automated synthesis function that generates correct suppression monitors from any formula taken from this logical fragment.