1 research outputs found
Inadmissible Class of Boolean Functions under Stuck-at Faults
Many underlying structural and functional factors that determine the fault
behavior of a combinational network, are not yet fully understood. In this
paper, we show that there exists a large class of Boolean functions, called
root functions, which can never appear as faulty response in irredundant
two-level circuits even when any arbitrary multiple stuck-at faults are
injected. Conversely, we show that any other Boolean function can appear as a
faulty response from an irredundant realization of some root function under
certain stuck-at faults. We characterize this new class of functions and show
that for n variables, their number is exactly equal to the number of
independent dominating sets (Harary and Livingston, Appl. Math. Lett., 1993) in
a Boolean n-cube. We report some bounds and enumerate the total number of root
functions up to 6 variables. Finally, we point out several open problems and
possible applications of root functions in logic design and testing