
Accession Number : AD0271038
Title : ON LINEAR EXTENSIONS OF THE CANONICAL PARTIAL ORDER IN THE NCUBE Q TO THE NTH POWER
Corporate Author : LOCKHEED MISSILES AND SPACE CO SUNNYVALE CALIF
Personal Author(s) : HU,SZETSEN
Report Date : OCT 1961
Pagination or Media Count : 1
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)
Descriptors : *FUNCTIONS(MATHEMATICS), *LINEAR SYSTEMS, *MATHEMATICAL LOGIC, ALGEBRA, COMPLEX VARIABLES, CRYSTAL LATTICES, INEQUALITIES, NUMBER THEORY, REAL VARIABLES
Distribution Statement : APPROVED FOR PUBLIC RELEASE