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, e.g., Journal
IEEE Transactions on Computers
Volume
C-28
Issue
10
Citation/Publisher Attribution
Lamagna, Edmund A.. "The Complexity of Monotone Networks for Certain Bilinear Forms, Routing Problems, Sorting, and Merging." IEEE Transactions on Computers C-28, 10 (1979): 773-782. doi: 10.1109/TC.1979.1675245.
