Inadmissible Class of Boolean Functions under Stuck-at Faults

Debesh K. Das; Debabani Chowdhury; Bhargab B. Bhattacharya; Tsutomu Sasao

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arXiv · 1309.3993

Inadmissible Class of Boolean Functions under Stuck-at Faults

Debesh K. Das·Debabani Chowdhury·Bhargab B. Bhattacharya·Tsutomu Sasao

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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.

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Debesh K. Das, Debabani Chowdhury, Bhargab B. Bhattacharya, Tsutomu Sasao. 2013-09-02. Inadmissible Class of Boolean Functions under Stuck-at Faults. https://arxiv.org/abs/1309.3993

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