Efficient Detection of Restricted Classes of Global Predicates

We show that the problem of predicate detection in distributed systems is NP-complete. We introduce a class of predicates, linear predicates, such that for any linear predicate B there exists an efficient detection of the least cut satisfyingB. The dual of linearity is post-linearity. These properties generalize several known properties of distributed systems, such as the set of consistent cuts forms a lattice, and the WCP and GCP predicate dectection results given in earlier work. We define a more general class of predicates, semi-linear predicates, for which efficient algorithms are known to detect whether a predicate has occurred during an execution of a distributed program. However, these methods may not identify the least such cut. Any stable predicate is an example of a semi-linear predicate. In addition, we show that certain unstable predicates can also be semi-linear, such as mutual exclusion violation. Finally, we show application of max-flow to the predicate detection problem. This result solves a previously open problem in predicate detection, establishing the existence of an efficient algorithm to detect predicates of the form x1 + x2 : : : + xN < k where xi are variables on different processes, k is some constant, and N is larger than 2. keywords: distributed debugging, predicate detection, unstable predicates. supported in part by the Texas Instruments/Jack Kilby Faculty Fellowship and by NSF Grant CCR-9409736 ysupported in part by the NSF Grant CCR-9110605, a TRW faculty assistantship award, a General Motors Fellowship, and an IBM grant