Defect-tolerant Systems Research Articles

Defect Tolerance: Fundamental Limits and Examples

This paper addresses the problem of adding redundancy to a collection of physical objects so that the overall system is more robust to failures. In contrast to its information counterpart, which can exploit parity to protect multiple information symbols from a single erasure, physical redundancy can only be realized through duplication and substitution of objects. We propose a bipartite graph model for designing defect-tolerant systems, in which the defective objects are replaced by the judiciously connected redundant objects. The fundamental limits of this model are characterized under various asymptotic settings and both asymptotic and finite-size systems that approach these limits are constructed. Among other results, we show that the simple modular redundancy is in general suboptimal. As we develop, this combinatorial problem of defect tolerant system design has a natural interpretation as one of graph coloring, and the analysis is significantly different from that traditionally used in information redundancy for error-control codes.

Evaluating the reliability of NAND multiplexing with PRISM

Probabilistic-model checking is a formal verification technique for analyzing the reliability and performance of systems exhibiting stochastic behavior. In this paper, we demonstrate the applicability of this approach and, in particular, the probabilistic-model-checking tool PRISM to the evaluation of reliability and redundancy of defect-tolerant systems in the field of computer-aided design. We illustrate the technique with an example due to von Neumann, namely NAND multiplexing. We show how, having constructed a model of a defect-tolerant system incorporating probabilistic assumptions about its defects, it is straightforward to compute a range of reliability measures and investigate how they are affected by slight variations in the behavior of the system. This allows a designer to evaluate, for example, the tradeoff between redundancy and reliability in the design. We also highlight errors in analytically computed reliability bounds, recently published for the same case study.