Approximation of δ-Timeliness

In asynchronous message-passing distributed systems prone to process crashes, a communication link is said δ-timely if the communication delay on this link is bounded by some constant δ. We study here in which way processes may approximate and find structural properties based on δ-timeliness (e.g., find δ-timely paths between processes or build a ring between correct processes using only δ-timely links). To that end, we define a notion of approximation of predicates. Then, with help of such approximations, we give a general algorithm that enables to choose and eventually agree on one of these predicates. Finally, applying this approach to δ-timeliness, we give conditions and algorithms to approximate δ-timeliness and dynamically find structural properties using δ-timeliness.