Double Fixed-Polarity Reed-Muller Expressions: A New Class of AND-EXOR Expressions for Compact and Testable Realization

As classes of AND-EXOR expressions, PPRMs, FPRMs, and ESOPs are well-known. In this paper, a new class of AND-EXOR expressions, Double Fixed-Polarity Reed-Muller Expressions (DFPRMs), is proposed. DFPRMs are generalized expressions of FPRMs, and can be the smallest PLA among all the classes of AND-EXOR expressions. We discuss their properties: the relation to other classes, a compact realization with (AND/OR)-EXOR PLAs, and the easy testability of the PLA. We show that all the stuck-at faults in DFPRM PLAs are detected by (2n+4) tests, which are independent of the functions realized by the PLAs. And we demonstrate the compactness of DFPRMs by giving a table of the number of products of the minimum DFPRMs for all 4-variable functions. The table is obtained by a minimization algorithm presented in this paper.