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Bounds on the Length of Terminal Stuck-Fault Test
March 1972 (vol. 21 no. 3)
pp. 305-309
C. Dennis Weiss, Department of Electrical Engineering, Johns Hopkins University, Baltimore, Md. 21218.
A terminal stuck fault in a logic network is represented by one or more stuck-at-1 or stuck-at-0 faults on the n input lines or single output. It is shown that for n ¿ 5, a least upper bound on the test length is n + 1, and for n ≫ 5, an upper bound is 2n - 4. A greatest lower bound is 3, for all n ≫ 1. The upper bounds are based on a maximum size alternating 1-tree in the n-cube representation of the function. Of the more than 600 000 equivalence classes of functions of n variables, n ¿ 5, only one does not have an n-edge alternating 1-tree. An algorithm is proposed for constructing tests based on alternating 1-trees.
Citation:
C. Dennis Weiss, "Bounds on the Length of Terminal Stuck-Fault Test," IEEE Transactions on Computers, vol. 21, no. 3, pp. 305-309, March 1972, doi:10.1109/TC.1972.5008955
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