Multi-level logic minimization using implicit don´t cares

An approach is described for the minimization of multilevel logic circuits. A multilevel representation of a block of combinational logic is defined, called a Boolean network. A procedure is then proposed, called ESPRESSOMLD, to transform a given Boolean network into a prime, irredundant, and R-minimal form. This procedure rests on the extension of the notions of primality and irredundancy, previously used only for two-level logic minimization, to combinational multilevel logic circuits. The authors introduce the concept of R-minimality, which implies minimality with respect to cube reshaping, and demonstrate the crucial role played by this concept in multilevel minimization. Theorems are given that prove the correctness of the proposed procedure. Finally, it is shown that prime and irredundant multilevel logic circuits are 100% testable for input and output single-stuck faults, and that these tests are provided as a byproduct of the minimization