
Accession Number : AD0654193
Title : ANALYSIS OF SYNTHESIS OF MULTITHRESHOLD LOGIC.
Descriptive Note : Final rept.,
Corporate Author : PURDUE UNIV LAFAYETTE IND SCHOOL OF ELECTRICAL ENGINEERING
Personal Author(s) : Fu,K. S. ; Mow,W. C. W.
Report Date : JUN 1967
Pagination or Media Count : 164
Abstract : The thesis treats a generalization of the concept of linearlyseparable (singlethreshold) Boolean functions, multithreshold functions. Some invariance operations peculiar to the multithreshold functions are shown to exist. Necessary and sufficient conditions of selfdual and selfcomplementary dual functions are obtained in terms of the multithreshold weight threshold vector. In particular, selfdual and selfcomplementary dual functions are shown to be realizable by odd and even number of effective thresholds only. It is shown that an n + 1 variable selfdual and selfcomplementary dual can be generated from an n variable Boolean function. Such generation of selfdual and selfcomplementary dual functions are shown to correspond to the functional forms of selfdualization and selfcomplementary dualization of an nvariable Boolean function. An algorithm for the synthesis of multithreshold threshold elements is presented. Instead of solving the set of linear inequalities, where the unknowns are the weights corresponding to the input variables, incremental weights are sought. The procedure reduces to that of resolving contradicting pairs of vertices by the incremental weights. The procedure is valid for linearly separable and nonlinearly separable Boolean functions. For the synthesis of arbitrary Boolean functions with a network of single threshold elements, compound and cascade threshold element syntheses from the multithreshold weight threshold vector are discussed. Finally, an improved tabulation of the multithreshold weight threshold vectors on the 221 equivalence classes of fourvariable Boolean functions under the NPN operation is included. (Author)
Descriptors : (*SPECIAL FUNCTIONS(MATHEMATICAL), ANALYSIS), EQUATIONS, SYNTHESIS, THEOREMS, DIGITAL COMPUTERS, TABLES(DATA), MATRICES(MATHEMATICS)
Subject Categories : Theoretical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE