On completely robust path delay fault testable realization of logic functions

A large class of Boolean functions, as well as almost all symmetric Boolean functions, are shown to have no two-level completely robust path-delay-fault testable (RPDFT) realization by combinational circuits. Exact and asymptotic formulae are derived for the number of symmetric Boolean functions which have two-level completely RPDFT realization. To achieve completely RPDFT realization, a notion of RPDFT-extension is proposed for logic functions which have no two-level completely RPDFT realization. Algorithms are devised for the design of RPDFT-extensions with at most 2 extra input variables.