Optimal Design of Checks for Error Detection and Location in Fault Tolerant Multiprocessor Systems

Abstract

Designing checks to detect or locate errors in the data is an important problem and plays an important role in the area of fault tolerance. Our checks are assumed to be of the simplest kind, i.e. a check can operate without any restriction on any non-empty subset of the set of data elements and can reliably detect up to one error in this subset. In this paper, we show how to design the data-check (DC) relationship. For the first time, we give a general procedure for designing checks to locate s errors, given any value for s. We also consider the problem of designing checks to detect s errors in the data. We give the first optimal construction for this problem. The procedure for designing the checks are simple and novel. One can also modify these constructions to produce uniform checks, i.e. checks which are identical and check the same number of data elements. We give procedures for obtaining such checks as well.Recently, the problem of designing the DC relationship has attracted a lot of attention due to the important role it plays in the design of algorithm-based fault tolerant (ABFT) systems. In this paper, we illustrate the above problem in this context. ABFT schemes have been shown to be a natural paradigm for concurrent error detection/location in multiprocessor systems and systolic array computations. Banerjee and Abraham have shown that an ABPT scheme can be modeled as a tripartite graph consisting of processors (P), data (D) and checks(C). Our constructions can be used along with any general technique for designing fault tolerant PDC graphs, e.g. for designing unit systems [NA89] or for designing ud-systems [VJ91] etc.KeywordsData ElementFault ToleranceConcurrent Error DetectionTripartite GraphFaulty ProcessorThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.