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Title: Small fan-in is beautiful

Abstract

The starting points of this paper are two size-optimal solutions: (1) one for implementing arbitrary Boolean functions; and (2) another one for implementing certain subclasses of Boolean functions. Because VLSI implementations do not cope well with highly interconnected nets -- the area of a chip grows with the cube of the fan-in -- this paper will analyze the influence of limited fan-in on the size optimality for the two solutions mentioned. First, the authors will extend a result from Horne and Hush valid for fan-in {Delta} = 2 to arbitrary fan-in. Second, they will prove that size-optimal solutions are obtained for small constant fan-ins for both constructions, while relative minimum size solutions can be obtained for fan-ins strictly lower that linear. These results are in agreement with similar ones proving that for small constant fan-ins ({Delta} = 6...9) there exist VLSI-optimal (i.e., minimizing AT{sup 2}) solutions, while there are similar small constants relating to the capacity of processing information.

Authors:
;
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE Assistant Secretary for Management and Administration, Washington, DC (United States)
OSTI Identifier:
658318
Report Number(s):
LA-UR-97-3493; CONF-980538-
ON: DE98000277; TRN: AHC2DT06%%202
DOE Contract Number:  
W-7405-ENG-36
Resource Type:
Conference
Resource Relation:
Conference: IEEE world congress on computational intelligence, Anchorage, AK (United States), 5-9 May 1998; Other Information: PBD: Sep 1997
Country of Publication:
United States
Language:
English
Subject:
99 MATHEMATICS, COMPUTERS, INFORMATION SCIENCE, MANAGEMENT, LAW, MISCELLANEOUS; NEURAL NETWORKS; INTEGRATED CIRCUITS; FUNCTIONS; IMPLEMENTATION; DIGITAL SYSTEMS; ANALOG SYSTEMS

Citation Formats

Beiu, V, and Makaruk, H E. Small fan-in is beautiful. United States: N. p., 1997. Web.
Beiu, V, & Makaruk, H E. Small fan-in is beautiful. United States.
Beiu, V, and Makaruk, H E. 1997. "Small fan-in is beautiful". United States. https://www.osti.gov/servlets/purl/658318.
@article{osti_658318,
title = {Small fan-in is beautiful},
author = {Beiu, V and Makaruk, H E},
abstractNote = {The starting points of this paper are two size-optimal solutions: (1) one for implementing arbitrary Boolean functions; and (2) another one for implementing certain subclasses of Boolean functions. Because VLSI implementations do not cope well with highly interconnected nets -- the area of a chip grows with the cube of the fan-in -- this paper will analyze the influence of limited fan-in on the size optimality for the two solutions mentioned. First, the authors will extend a result from Horne and Hush valid for fan-in {Delta} = 2 to arbitrary fan-in. Second, they will prove that size-optimal solutions are obtained for small constant fan-ins for both constructions, while relative minimum size solutions can be obtained for fan-ins strictly lower that linear. These results are in agreement with similar ones proving that for small constant fan-ins ({Delta} = 6...9) there exist VLSI-optimal (i.e., minimizing AT{sup 2}) solutions, while there are similar small constants relating to the capacity of processing information.},
doi = {},
url = {https://www.osti.gov/biblio/658318}, journal = {},
number = ,
volume = ,
place = {United States},
year = {1997},
month = {9}
}

Conference:
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