Journal ArticleDOI
A Topological Method for the Determination of the Minimal Forms of a Boolean Function
R. H. Urbano,R. K. Mueller +1 more
TLDR
A numerical easily programmed procedure is given with which it is possible to treat problems with a greater number of variables than has heretofore been practical.Abstract:
The topology of the n-dimensional cube is used to reduce the problem of determining the minimal forms of a Boolean function of n variables to that of finding the minimal coverings of the essential vertices of the basic cell system associated with the given function. The proof of this statement is contained in the central Theorem 4. A numerical easily programmed procedure is given with which it is possible to treat problems with a greater number of variables than has heretofore been practical. The procedure by-passes the determination of the basic cells (the prime implicants of W. V. Quine) and locates the essential vertices, from which in turn the irredundant and minimal forms are obtained.read more
Citations
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Journal ArticleDOI
The lattice theory of Post algebras
Proceedings ArticleDOI
SOCRATES: A System for Automatically Synthesizing and Optimizing Combinational Logic
TL;DR: SOCRATES optimizes logic using boolean and algebraic minimization techniques, and it optimizes circuits derived from this logic in a user defined technology with a rule based expert system.
Journal ArticleDOI
Pattern-Based Modeling and Solution of Probabilistically Constrained Optimization Problems
TL;DR: Results show that large-scale stochastic problems, in which up to 50,000 scenarios are used to describe the stochastics variables, can be consistently solved to optimality within a few seconds.
Journal ArticleDOI
Irredundant disjunctive and conjunctive forms of a Boolean function
TL;DR: A thorough algebraic method is described for the determination of the complete set of irredundant normal and conjunctive forms of a Boolean function that is mechanical and therefore highly programmable on a computer.
Journal ArticleDOI
Polynomial-time algorithms for generation of prime implicants
TL;DR: It is shown that all presented algorithms are polynomial in the number of minterms occurring in the canonical disjunctive normal form representation of a Boolean function.
References
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Journal ArticleDOI
A symbolic analysis of relay and switching circuits
TL;DR: It will be shown that several of the well-known theorems on impedance networks have roughly analogous theorem in relay circuits, including the delta-wye and star-mesh transformations, and the duality theorem.
Journal ArticleDOI
The Problem of Simplifying Truth Functions
TL;DR: The Problem of Simplifying Truth Functions is concerned with the problem of reducing the number of operations on a graph to a simple number.
Journal ArticleDOI
Application of Boolean algebra to switching circuit design and to error detection
TL;DR: It is shown that certain parts of the multiple output problem for switching circuits that have more than one output may be reduced to a single output problem whose inputs are equal in number to the sum of the numbers of inputs and outputs in the original problem.
Journal ArticleDOI
Switching functions on an n-dimensional cube
TL;DR: This paper considers 2-terminal combinational networks from a somewhat different viewpoint, mainly a switching function will be considered as a set of Vertexes on an n-dimensional cube (n-cube).