Composition of multiple faults in RAMs

Abstract

Single cell-array faults in RAMs are usually represented by Mealy automata. Multiple faults should also be representable by automata; in fact, it should be possible to compute the automaton of a multiple fault from the automata of the single faults that make up the multiple fault. We study properties of binary composition operations on automata for the representation of multiple faults in RAMs. First, we derive a set of generic conditions that every composition operation must satisfy. Second, we develop a set of physical conditions that the composition must satisfy in order to apply to stuck-at, transition and coupling faults in RAMs. Third, we represent the transition table rules used by van de Goor and Smit (1993, 1994) by a composition operation and prove that this operation satisfies both the generic and physical conditions. Fourth, we point out that it may be appropriate to use a different composition operation to permit a different handling of coupling faults in the presence of stuck-at or transition faults.