Testability of generalized multiple-valued Reed-Muller circuits

Abstract

The testability of generalized Reed-Muller circuits realizing m-valued functions in module m sum-of-product form, with m being a prime greater than two, is investigated. Two aspects of the problem are considered-the number of tests required for fault detection, and the generation of tests. We prove that just four tests are sufficient to detect all single stuck-at faults on internal lines in the circuit. Furthermore, this set of tests is independent of the function being realized and therefore universal. We give two alternative techniques for testing primary inputs-one by generating a test set of maximum length 2n, where n is the number of primary inputs and the other by adding to the circuit an extra multiplication mod m gate with an observable output to ensure that the four tests for internal lines also detect all single stuck-at faults on primary inputs.