Delay-fault testability preservation of the concurrent decomposition and factorization transformations

Recently, a new, very efficient method of multilevel logic synthesis based on factorization and decomposition of Boolean expressions has been introduced. It has been shown that the transformations used by this method preserve the single stuck-at testability of two-level circuits. In this paper, we show that single-cube extraction, double-cube extraction, and dual-extraction of double-cubes ∈ D_1,1,2 and D_2,2,2 preserve testability with respect to a general robust path-delay-fault (RPDF) test set. However, we show that while dual-expansion of double-cubes ∈ D_2,2,3 preserves RPDF testability of paths through the extracted divisors with respect to a single-input-changing test set, it does not guarantee RPDF testability preservation of unmodified paths. Furthermore, we provide sufficient conditions for algebraic resubstitution with complement to preserve RPDF testability that cover a larger class of complementary expressions that was known previously. The testability preservation of these transformations is demonstrated on a set of RPDF testable Berkeley PLAs.