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This paper treats a fault detection/location of multi-processor systems, and we present a checking scheme based on Modified Processor-Data (MPD) graph with considering an error generation/propagation model for Algorithm-Based Fault Tolerant (ABFT) systems. The error propagation model considered here allows a computation result with multiple (more than one) erroneous inputs to be either erroneous or error-free. Also a basic algorithm for constructing checks for single-fault locatable/two-fault detectable ABFT systems based on the checking scheme is described with design examples.