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Binary Functions and their Applications

  • Book
  • © 1990

Overview

Authors:
  1. Horand Störmer

    1. Lehrstuhl für Mathematik V Fakultät für Mathematik und Informatik, Universität Mannheim, Mannheim 1, Germany

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Part of the book series: Lecture Notes in Economics and Mathematical Systems (LNE, volume 348)

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-viii
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  2. Introduction

    • Horand Störmer
    Pages 1-2

  3. Binary Functions and their Representations by Implicants

    • Horand Störmer
    Pages 3-22

  4. Representations of Binary Functions by Implicates

    • Horand Störmer
    Pages 23-35

  5. Reduction Methods

    • Horand Störmer
    Pages 36-43

  6. Discrete Functions

    • Horand Störmer
    Pages 44-79

  7. Applications

    • Horand Störmer
    Pages 80-83

  8. A Class of Finite Boolean Algebras

    • Horand Störmer
    Pages 84-109

  9. Applications

    • Horand Störmer
    Pages 110-142

  10. Concluding Remark

    • Horand Störmer
    Pages 143-143

  11. Back Matter

    Pages 144-156
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Keywords

About this book

In this book binary functions and their representation by implicants or implicates are described. In particular minimal representations by prime implicants or prime implicates are given. Such representations generalize the minimal representations of the usual Boolean functions. It is shown that implicants (implicates) of discrete functions may be constructed with the help of implicants (implicates) of binary functions. One substantial application is the description of the reliability structure of technical systems, another is the use of binary respectively discrete functions to classify objects which are described by the grades of certain attributes. Finally a class of Boolean algebras of practical importance (set algebras, indicator algebras, algebras of classes of propositions) are considered. The elements of such algebras have representations which are strongly connected with the representations of binary functions.

Authors and Affiliations

  • Lehrstuhl für Mathematik V Fakultät für Mathematik und Informatik, Universität Mannheim, Mannheim 1, Germany

    Horand Störmer

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