Inadmissible Class of Boolean Functions under Stuck-at Faults
Abstract
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.
Keywords
Cite
@article{arxiv.1309.3993,
title = {Inadmissible Class of Boolean Functions under Stuck-at Faults},
author = {Debesh K. Das and Debabani Chowdhury and Bhargab B. Bhattacharya and Tsutomu Sasao},
journal= {arXiv preprint arXiv:1309.3993},
year = {2013}
}