Electrical and Computer Engineering ETDs

Publication Date

7-31-1970

Abstract

This dissertation extends the theory of Ashenhurst and Curtis on complex disjunctive decompositions of Boolean functions. The extension takes this theory into the realm of incompletely specifies Boolean functions, that is, those with don-t-care conditions (phi’s). First, the theory is extended to a simple decomposition through a compatibility relation on incompletely specified Boolean vectors whose elements are 0’s, 1’s and phi’s. This relations is applied to the columns of the decomposition charts used by Curtis and Ashenhurst. To accomplish complex disjunctive decompositions, a new Boolean variable, called a constrained don’t-care is introduced as a component of a new Boolean vector called a constrained Boolean vector. This constrained vector is used to specify conditions on the assignments of the phi’s of the original function which are required by the process of decomposition. Finally, a criterion of merit is suggested for decomposition structures which leads to a choice among the many possible decomposition structures which may be formed to realize an incompletely specified switching function. Some results are presented specified switching function. Some results are presented which demonstrate the applicability of the theory of decomposition to the removal of unnecessary variables and to the detection of symmetric variables.

Document Type

Dissertation

Language

English

Degree Name

Computer Engineering

Level of Degree

Doctoral

Department Name

Electrical and Computer Engineering

First Committee Member (Chair)

Ronald Clifford DeVries

Second Committee Member

Illegible

Third Committee Member

Illegible

Third Advisor

Arnold Herman Koschmann

Download

Share

COinS