ON LINEAR EXTENSIONS OF THE CANONICAL PARTIAL ORDER IN THE N-CUBE Q TO THE NTH POWER

Abstract

The enumeration of the canonical truth functions is considered. A method of getting all of the canonical truth functions is given. The canonical partial order is studied in the Q to the Nth power and proven that Q to the Nth power becomes a lattice with respect to the canonical partial order. A recurrent method of constructing the lattice structure of Q to the Nth power is also given. The fact is established that the canonical partial order in Q to the Nth power can be extended to a linear order which will be called the principal linear order of Q to the Nth power. Since this linear order of Q to the Nth power can be defined by an injective canonical weight function, those linear orders of Q to the Nth power which can be defined by injective weight functions can be studied. A recurrent method of finding these linear orders of Q to the Nth power is given. These linear orders are applied to the problem of finding all canonical truth functions. (Author)

Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1961
Accession Number
AD0271038

Entities

People

  • Sze-tsen Hu

Organizations

  • Lockheed Martin Missiles and Space

Tags

Communities of Interest

  • Energy and Power Technologies

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.