Reliable Fault Diagnosis with Few Tests

Abstract

We consider the problem of fault diagnosis in multiprocessor systems. Processors perform tests on one another: fault-free testers correctly identify the fault status of tested processors, while faulty testers can give arbitrary test results. Processors fail independently with constant probability p < 1/2 and the goal is to identify correctly the status of all processors, based on the set of test results. For 0 < q < 1, q-diagnosis is a fault diagnosis algorithm whose probability of error does not exceed q. We show that the minimum number of tests to perform q-diagnosis for n processors is Θ(n log 1 q ) in the nonadaptive case and n + Θ(log 1 q ) in the adaptive case. We also investigate q-diagnosis algorithms that minimize the maximum number of tests performed by, and performed on, processors in the system, constructing testing schemes in which each processor is involved in very few tests. Our results demonstrate that the flexibility yielded by adaptive testing permits a significant saving in the number of tests for the same reliability of diagnosis.

Combinatorial Pair Testing: Distinguishing Workers from Slackers

“…One processor can check another, but the result of this check can only be trusted if the processor doing the testing is good. Often, in fact, one assumes that faulty processors deliberately misidentify the ones they are testing [5,17]. Beigel et al [2][3][4] show that if the number of faulty processors is sufficiently far below n/2, then O(n) tests can be organized into a sequence of O(1) parallel testing rounds, where each processor tests at most one other in each round, so as to identify all faulty processors.…”

Minimizing the number of inputs while applying adaptive test cases

“…State-based formalisms such as Finite State Machine and its derivatives have been used extensively for the specification of the externally observable behavior of a wide range of reactive systems [3][4][5][6][7]. A use of such specifications is to construct a set of test cases to be employed during testing of potential implementations of the specified system.…”

The worst-case chip problem

“…These problems have a long history and lengthy bibliography; Pelc and Upfal [8] give an excellent summary with a useful bibliography. In this paper we address only the question of finding a single good chip, assuming that the majority of the chips are good and that any chip can test any other.…”