Failure Detection Sequencers: Necessary and Sufficient Information about Failures to Solve Predicate Detection

This paper investigates the amount of information about failures needed to solve the predicate detection problem in asynchronous systems with crash failures. In particular, we show that predicate detection cannot be solved with traditional failure detectors, which are only functions of failures. In analogy to the definition of failure detectors, we define a failure detection sequencer, which can be regarded as a generalization of a failure detector. More specifically, our failure detection sequencer Σ outputs information about failures and about the final state of the crashed process. We show that Σ is necessary and sufficient to solve predicate detection. Moreover, Σ can be implemented in synchronous systems. Finally, we relate sequencers to perfect failure detectors and characterize the amount of knowledge about failures they additionally offer.