Title

The Complexity of Monotone Networks for Certain Bilinear Forms, Routing Problems, Sorting, and Merging

Document Type

Article

Date of Original Version

1-1-1979

Abstract

In this paper, we consider the size of combinational switching networks required to synthesize monotone Boolean functions using only operations from the functionally incomplete set of primitives {disjunction, conjunction}. A general methodology is developed which is used to derive Ω(n log n) lower bounds on the size of monotone switching circuits for certain bilinear forms (including Toeplitz and circulant matrix-vector products, and Boolean convolution), certain routing networks (including cyclic and logical shifting), and sorting and merging. A homomorphic mapping technique is also given whereby the lower bounds derived on the sizes of monotone switching networks for Boolean functions can be extended to a larger class of problem domains. Copyright © 1979 by the Institute of Electrical and Electronics Engineers, Inc.

Publication Title

IEEE Transactions on Computers

Volume

C-28

Issue

10

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