OPTIMAL-DESIGN OF CHECKS FOR ERROR-DETECTION AND LOCATION IN FAULT-TOLERANT MULTIPROCESSOR SYSTEMS

Designing checks to detect or locate errors in the data plays an important role in the design of fault tolerant systems. Recently, the problem of synthesizing the data-check (DC) relationship has received a lot of attention in the context of a natural paradigm for concurrent error detection/location known as algorithm-based fault tolerance (ABFT). Banerjee and Abraham have shown that an ABFT scheme can be modeled as a tripartite graph consisting of processors (P), data (D), and checks (C). Any technique for designing ABFT systems requires a procedure for synthesizing a DC relationship, which not only has a low overhead but also has all the properties required by the designer. The main contribution of this work is to propose a simple and novel algorithm called RANDGEN to generate DC graphs. This synthesis approach itself is very fast and can be fully parallelized. By simply varying its parameters, the same algorithm RANDGEN can produce DC graphs with a wide spectrum of properties, many of which have been considered very important in recent ABFT designs. RANDGEN produces s-error-detectable DC graphs with asymptotically the least number of checks for the first time. RANDGEN can also produce s-error-locatable DC graphs using only a small number of checks. This is the first general procedure for producing error-locatable graphs for any value of s. Another important outstanding problem in DC graph design is providing fast and practical methods for actually locating the errors in the data from the output pattern at the checks. We show that RANDGEN can be used to design DC graphs, which permit easy diagnosis, again with a small number of checks. It has been pointed out previously that ''uniform'' checks may simplify the design of the ABFT system. We show how RANDGEN can be modified very simply to produce uniform s-error-detectable/locatable DC graphs. Finally, we show how one can generalize these results to synthesize strictly s-error-detectable/locatable DC graphs which can detect/locate up to s data errors even when s or fewer check computations are erroneous.