Relationships between Post and Boolean Algebras with Application to Multi-Valued Switching Theory.

Abstract

The fundamentals of Post algebras are presented along with extensions that will be useful in a proposed multi-valued switching theory. A detailed examination of Post and Boolean functions is presented along with a functional representation that facilitates the comparison of Post and Boolean algebras. It is shown that Boolean functions of one variable can be represented as Post functions. The general relationships between Post and Boolean algebras are examined. The structure of Boolean subalgebras of Post algebras is discussed, with particular emphasis placed on algebras which are composed of Boolean and Post functions. A transformation between sets of Boolean functions and Boolean algebras of vectors is presented along with a further transformation from the Boolean algebras of vectors to sets of Post functions. The structure of equivalence classes of Post functions and their relationship to Boolean functions is examined. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1971
Accession Number
AD0726381

Entities

People

  • Anthony Stephen Wojcik

Organizations

  • University of Illinois Urbana–Champaign

Tags

DTIC Thesaurus Topics

  • Complex Variables
  • Functions (Mathematics)
  • Mathematical Analysis
  • Mathematics
  • Switching

Fields of Study

  • Mathematics

Readers

  • Energy Conservation and Renewable Energy Engineering.
  • Graph Algorithms and Convex Optimization.
  • Linear Algebra