(Im)Possibilities of Predicate Detection in Crash-Affected Systems

In an asynchronous system, where processes can crash, perfect predicate detection for general predicates is difficult to achieve. A general predicate thereby is of the form , where and refer to a normal process variable and to the operational state of that process, respectively. Indeed, the accuracy of predicate detection largely depends on the quality of failure detection. In this paper, we investigate the predicate detection semantics that are achievable for general predicates using either failure detector classes , , or . For this purpose, we introduce weaker variants of the predicate detection problem, which we call stabilizing and infinitely often accurate. We show that perfect predicate detection is impossible using the aforementioned failure detectors. Rather, and only allow stabilizing predicate detection. Consequently, we explore alternative approaches to perfect predicate detection: introducing a stronger failure detector, called ordered perfect, or restricting the general nature of predicates.