Bounds on the Length of Terminal Stuck-Fault Test

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.