Accession Number : AD0851857

Title :   The Lattice-Grid Network and its Applications to the Minimization and Threshold-Gate Realization of Boolean Switching Functions.

Descriptive Note : Master's thesis,

Corporate Author : AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH SCHOOL OF ENGINEERING

Personal Author(s) : Sandmore, Peter C.

Report Date : DEC 1968

Pagination or Media Count : 84

Abstract : The Lattice-Grid Network (LGN) is a 2-dimensional representation of the n-cube that is theoretically unbounded in the finite number of dimensions (variables) for which it can be constructed. The basis of the construction technique is that each row of the LGN contains all the vertices (minterms) that have the same number of '1' coordinates (uncomplemented variables). Techniques similar to those used with a Karnaugh Map are used with the LGN for the minimization of completely and incompletely specified Boolean functions of either single or multiple outputs. The LGN is also used to identify and determine the realization of threshold functions. A 'characteristic measure' of the function is determined, using a small fraction of the vertices of the function, to identify 2-monotonicity and evaluate the weights in the realization of the function. (n/2)-monotonicity, the final step in the process of identifying a threshold function, is determined using a visual technique of comparing the function with its dual. (Author)

Descriptors :   *SWITCHING CIRCUITS, *LOGIC CIRCUITS, OPTIMIZATION, ALGEBRA, GATES(CIRCUITS), FUNCTIONS(MATHEMATICS), THESES.

Subject Categories : Electrical and Electronic Equipment
      Cybernetics

Distribution Statement : APPROVED FOR PUBLIC RELEASE