Journal ArticleDOI
Boolean function minimization in the class of disjunctive normal forms
A. A. Sapozhenko,I. P. Chukhrov +1 more
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The survey focuses on minimization of boolean functions in the class of disjunctive normal forms (d.n.f.s) and covers the publications from 1953 to 1986, and presents a classification of minimization algorithms.Abstract:
The survey focuses on minimization of boolean functions in the class of disjunctive normal forms (d.n.f.s) and covers the publications from 1953 to 1986. The main emphasis is on the mathematical direction of research in boolean function minimization: bounds of parameters of boolean functions and algorithmic difficulties of minimal d.n.f. synthesis). The survey also presents a classification of minimization algorithms and gives some examples of minimization heuristics with their efficiency bounds.read more
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Journal ArticleDOI
Computational complexity of Boolean functions
TL;DR: The purpose of this survey is to give an account of the main results over the last sixty years related to the complexity of computation (realization) of Boolean functions by contact networks, Boolean circuits, and Boolean circuits without branching.
Journal ArticleDOI
Implementation of Boolean functions with a bounded number of zeros by disjunctive normal forms
Yu. V. Maximov,Yu. V. Maximov +1 more
TL;DR: The problem of constructing simple disjunctive normal forms (DNFs) of Boolean functions with a small number of zeros is considered and a key idea of the reduction method is that a Boolean function is represented as a disjunction of Boolean function with fewer zeros.
Journal ArticleDOI
Connected Boolean Functions with a Locally Extremal Number of Prime Implicants
TL;DR: In this article, the authors studied the properties of connected Boolean functions with many prime implicants and introduced the notion of a locally extremal function in a certain neighborhood in terms of the number of implicant ranks.
Journal ArticleDOI
On irredundant complexes of faces in the unit cube
TL;DR: In this paper, the authors proposed a probabilistic approach to construct and estimate the cardinality of sets of irredundant complexes of faces, which can be used for estimation of the maximum values of the length and the number of disjunctive normal forms in the class of d.n.f.
Journal ArticleDOI
On the Complexity of Minimizing Quasicyclic Boolean Functions
TL;DR: In this article, the authors investigate the Boolean functions that combine various properties: the extremal values of complexity characteristics of minimization, the inapplicability of local methods for reducing the complexity of the exhaustion, and the impossibility to efficiently use sufficient minimality conditions.
References
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Proceedings ArticleDOI
The complexity of theorem-proving procedures
TL;DR: It is shown that any recognition problem solved by a polynomial time-bounded nondeterministic Turing machine can be “reduced” to the problem of determining whether a given propositional formula is a tautology.
Journal ArticleDOI
Minimization of Boolean functions
TL;DR: A systematic procedure is presented for writing a Boolean function as a minimum sum of products and specific attention is given to terms which can be included in the function solely for the designer's convenience.
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
A Way to Simplify Truth Functions
TL;DR: In this paper, a way to simplify truth functions is proposed. But it is difficult to verify the correctness of truth functions and it is not easy to find the truth functions in practice.
Journal ArticleDOI
The map method for synthesis of combinational logic circuits
TL;DR: The problem in this area which has been attacked most energetically is that of the synthesis of efficient combinational that is, nonsequential, logic circuits.