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A Sufficient Condition for Detecting ANDOR-AND-Type Logic

Three-level logic is shown to have a potential for reduction of the area over two-level implementations, as well as for a gain in speed over multi-level implementations. Algorithms for finding AND-OR-XOR and AND-OR-AND expressions were developed, however an open problem remained which of the algorithms should be used to find an optimal solution for a given function. In this paper we formulate a sufficient condition for a function to have a decomposition of type , with the total number of products in , and smaller or equal than the number of products in . This condition is used to design an algorithm for deciding whether a function is likely to have a compact AND-OR-XOR expression.