Hyper Parametric Timed CTL

Abstract

Hyperproperties enable simultaneous reasoning about multiple execution traces of a system and are useful to reason about noninterference, opacity, robustness, fairness, observational determinism, etc. We introduce hyper parametric timed computation tree logic (HyperPTCTL), extending hyperlogics with timing reasoning and, notably, parameters to express unknown values. We mainly consider its nest-free fragment, where the temporal operators cannot be nested. However, we allow extensions that enable counting actions and comparing the duration since the most recent occurrence of specific actions. We show that our nest-free fragment with this extension is sufficiently expressive to encode the properties, e.g., opacity, (un)fairness, or robust observational (non)determinism. We propose semi-algorithms for the model checking and synthesis of parametric timed automata (TAs) (an extension of TAs with timing parameters) against this nest-free fragment with the extension via reduction to the PTCTL model checking and synthesis. While the general model checking (and thus synthesis) problem is undecidable, we show that a large part of our extended (yet nest-free) fragment is decidable, provided the parameters only appear in the property, not in the model. We also exhibit additional decidable fragments where the parameters within the model are allowed. We implemented our semi-algorithms on the top of the IMITATOR model checker and performed experiments. Our implementation supports most of the nest-free fragments (beyond the decidable classes). The experimental results highlight our method’s practical relevance.