On the Number of Functions Realized by Cascades and Disjunctive Networks

Abstract

In this paper, the number of functions realized by certain networks of two-input one-output gates are presented. Two networks are considered; one is the disjunctive network, which is characterized by the restriction that each gate output and each network input connect to exactly one gate input. The other network, the cascade, is the special case of the disjunctive networks in which each gate has at least one input which connects to a network input. For both networks, a recursion relation is derived for the number of realized switching functions dependent on exactly kappa variables. Both expressions have been solved by computer for kappa up to 15. Also, expressions are derived for the number of functions realized by cascades and disjunctive networks of two-input one-output cells, where each cell realizes any of the 16 functions on two variables.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1975
Accession Number
ADA605509

Entities

People

  • Jon T. Butler

Organizations

  • Naval Postgraduate School

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DTIC Thesaurus Topics

  • Air Force
  • Air Force Facilities
  • Breeding
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  • Computers
  • Decomposition
  • Digital Computers
  • Electrical Engineering
  • Engineering
  • Exclusion Principle
  • Exponential Functions
  • Graph Theory
  • Index Terms
  • Infinite Series
  • Permutations
  • Switching
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Fields of Study

  • Computer science

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  • Computer Programming and Software Development.
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