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On the Properties of Irredundant logic Networks

IEEE Transactions on Computers 1976年第9期C-25卷 884-892页

作者： Hayes, John P. Department of Electrical Engineering Computer Science Program University of Southern California Los Angeles CA 90007 United States

The constraints imposed by various types of irredundancy on the structure of combinational logic networks are investigated. It is shown that the usual notion ofirredundancy here called a-irredundancy, places bounds on the maximum number of inputs to certain types of network structures. A network is called b-redundant if it contains a cascade of single-input gates that can be reduced to either an inverter or a single line. Let Nab(Z) denote all realizations of Z that are both a - and b-irredundant. If N E Nab(Z), then the number of gates in any fan-out-free subnetwork of N is bounded. It is shown that a solution to some important design optimization problems can be found in Nab(Z). It is conjectured that Nab(Z) is finite and some results supporting this conjecture are presented. For example, it is impossible to construct an arbitrarily long cascade of networks that perform the identity transformation without introducing a-or b-redundancy. A more general type of redundancy, c-redundancy, is defined which includes both a-and b-redundancy as special cases. The class of c-irredundant realizations of Z is finite. Copyright © 1976 by The Institute of Electrical and Electronics Engineers, Inc.

关键词： Combinational networks irredundant networks logic circuits logic design optimization redundancy redundancy testing redundancy types

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