Deeper and sparser nets are optimal

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The starting points of this paper are two size-optimal solutions: (1) one for implementing arbitrary Boolean functions (Home and Hush, 1994); and (2) another one for implementing certain sub-classes of Boolean functions (Red`kin, 1970). Because VLSI implementations do not cope well with highly interconnected nets--the area of a chip grows with the cube of the fan-in (Hammerstrom, 1988)--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 Home and Hush (1994) valid for fan-in {Delta} = 2 to arbitrary fan-in. Second, they will prove ... continued below

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10 p.

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Beiu, V. & Makaruk, H.E. March 1, 1998.

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Description

The starting points of this paper are two size-optimal solutions: (1) one for implementing arbitrary Boolean functions (Home and Hush, 1994); and (2) another one for implementing certain sub-classes of Boolean functions (Red`kin, 1970). Because VLSI implementations do not cope well with highly interconnected nets--the area of a chip grows with the cube of the fan-in (Hammerstrom, 1988)--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 Home and Hush (1994) valid for fan-in {Delta} = 2 to arbitrary fan-in. Second, they will prove that size-optimal solutions are obtained for small constant fan-in 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 (Beiu, 1997a), while there are similar small constants relating to the capacity of processing information (Miller 1956).

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10 p.

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OSTI as DE98003447

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  • EIS `97: international symposium on engineering of intelligent systems, Tenerife (Spain), 11-13 Feb 1998

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  • Other: DE98003447
  • Report No.: LA-UR--97-4359
  • Report No.: CONF-980216--
  • Grant Number: W-7405-ENG-36
  • Office of Scientific & Technical Information Report Number: 645481
  • Archival Resource Key: ark:/67531/metadc694615

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  • March 1, 1998

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  • Aug. 14, 2015, 8:43 a.m.

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  • May 5, 2016, 6:24 p.m.

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Beiu, V. & Makaruk, H.E. Deeper and sparser nets are optimal, article, March 1, 1998; New Mexico. (digital.library.unt.edu/ark:/67531/metadc694615/: accessed November 22, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.