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Eugene L. Lawler

Bio: Eugene L. Lawler is an academic researcher. The author has contributed to research in topics: Implicant & Maximum satisfiability problem. The author has an hindex of 1, co-authored 1 publications receiving 5 citations.

Papers
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Proceedings ArticleDOI
07 Oct 1962
TL;DR: This paper presents a new approach to the problem of multi-level Boolean minimization, extended to minimal expressions with more than three levels and to "absolute" minimal expressions.
Abstract: This paper presents a new approach to the problem of multi-level Boolean minimization. Conventional two-level minimization methods are embedded in a process that makes extensive use of the properties of incompletely specified functions. Particular attention is given to the problem of obtaining minimal sums-of-products-of-sums. Then the approach is extended to minimal expressions with more than three levels and to "absolute" minimal expressions. Several examples are worked out.

5 citations


Cited by
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Journal ArticleDOI
TL;DR: Factoring techniques are incorporated in computer-oriented algorithms for the synthesis of fan-in limited NAND switching networks and tree networks with reduced gate count or levels of logic are sought.
Abstract: Factoring techniques are incorporated in computer-oriented algorithms for the synthesis of fan-in limited NAND switching networks. Tree networks with reduced gate count or levels of logic are sought. While example FORTRAN programs emphasize computer execution of the algorithms, they are also efficient for hand execution.

52 citations

Journal ArticleDOI
TL;DR: A method for determining the ps maximal implicants of a function is described and it is important to note that the knowledge of the second-stage functions is not necessary for the determination of the minimal third-order expressions of the functions considered in the examples, but it could not prove this to be a general property.
Abstract: ``ps maximal implicant'' of a function T is every function F having the following properties: 1) F implies TX; 2) the cost of the minimal ``product of sums of literals'' expression of F (ps M F) is inferior to the cost of the minimal ``product of sums of literals'' of T (ps M T); 3) no function V, implying T and implied by F, has a ps expression whose cost is inferior to the cost of the ps M F. ps maximal implicants have, for the third-order minimization, the same importance that conventional prime implicants have for the second-order minimization. In this paper a method for determining the ps maximal implicants of a function is described. The procedure consists in the determination of two sets of functions, called ``first-stage'' and ``second-stage functions,'' and in the search for ps maximal implicants among the complements of those functions. While the determination of the first-stage functions offers no difficulty, the problem of finding the second-stage functions is an intricate one. However, it can be solved by a topological approach. It is important to note that the knowledge of the second-stage functions is not necessary for the determination of the minimal third-order expressions of the functions considered in the examples, but we could not prove this to be a general property.

2 citations

Proceedings ArticleDOI
11 Nov 1964
TL;DR: In this paper a method is presented for reducing the number of stages of logic in the realization of an arbitrary Boolean function when an upper bound exists on the fan-in at each gate.
Abstract: In this paper a method is presented for reducing the number of stages of logic in the realization of an arbitrary Boolean function when an upper bound exists on the fan-in at each gate. A procedure for obtaining the minimum stage realization of the function in sum of products form is first developed. The use of factoring to reduce the number of stages below this minimum is then described.

1 citations