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Journal ArticleDOI

Clause-Column Table Approach for Generating All the Prime Implicants of Switching Functions

01 Nov 1972-IEEE Transactions on Computers (IEEE)-Vol. 21, Iss: 11, pp 1239-1246
TL;DR: This note describes an iterative procedure for generating the prime implicants of switching functions by utilizing a new tabular mode of functional representation called clause-column table, which can be applied equally well to functions given in the sum-of-products or in the product- of-sums froms.
Abstract: This note describes an iterative procedure for generating the prime implicants of switching functions by utilizing a new tabular mode of functional representation called clause-column table. The procedure generates all the prime implicants and can be applied equally well to functions given in the sum-of-products or in the product-of-sums froms, both canonical and noncanonical. The procedure can also be readily adapted to determine the prime implicants of functions having a large number of unspecified or DON'T CARE terms.
Citations
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Journal ArticleDOI
TL;DR: The problem of minimizing the bit dimension of control memories in microprogrammed digital computers is considered and the set of maximum compatibility classes of microcommands whose number is usually small is started, and near-minimal irredundant solutions are obtained.
Abstract: The problem of minimizing the bit dimension of control memories in microprogrammed digital computers is considered in this paper. We start essentially with the same basic formulation as that of Grasselli and Montanari [2]. However, in order to minimize the computational requirements, we start directly with the set of maximum compatibility classes of microcommands whose number is usually small, and readily obtain near-minimal irredundant solutions. A minimal solution is then obtained from the irredundant solutions.

60 citations

Journal ArticleDOI
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.

54 citations

Journal ArticleDOI
01 May 1989
TL;DR: Thelen's algorithm has been applied to the logic design of two-level multiple-output switching circuits as discussed by the authors, where the expansion of implicants, detection of essential primes, computation of a minimal cover and reduction of prime implicant can be reduced to one problem and efficiently solved by the use of Thelen's algorithms.
Abstract: The paper presents Thelen's algorithm (1981) and its application to the (1981) problems which arise in the logic design of two-level multiple-output switching circuits. The paper shows that the logic minimisation procedures, such as the expansion of implicants, detection of essential primes, computation of a minimal cover and reduction of prime implicants can be reduced to one problem and efficiently solved by the use of Thelen's algorithm. Based on these new procedures the author presents two heuristic minimisation algorithms, an iterative Espresso-like minimiser and a very fast one-pass minimiser, and discusses their results. Both minimiser differ from known algorithms in that minimisation is based on only one fundamental (easily programmable) procedure and minimisation of incompletely specified Boolean functions is performed without use of the don't care set. Because of the latter aspect the design algorithms are especially suited for the minimisation of logic functions whose don't care set is large and/or not explicitly given. The algorithms have been successfully tested in the design of finite state machines and are part of the CAD-system CARLOS, a logic synthesis system for the design of multilevel CMOS switching circuits.

33 citations

Journal Article
TL;DR: A new method of detecting deadlocks and traps in Petri nets using the search tree algorithm proposed by Thelen and some heuristics for Thelen’s method are presented.
Abstract: A new method of detecting deadlocks and traps in Petri nets is presented. Deadlocks and traps in Petri nets can be represented by the roots of special equations in CNF form. Such equations can be solved by using the search tree algorithm proposed by Thelen. In order to decrease the tree size and to accelerate the computations, some heuristics for Thelen’s method are presented.

22 citations

Journal ArticleDOI
TL;DR: It is shown that factoring accounts for a dramatic increase in efficiency over Nelson's algorithm, and the increased efficiency is illustrated with results obtained from several examples that were implemented for both algorithms using the symbolic manipulation systems SETS.
Abstract: An algorithm for finding the prime implicants of a Boolean function is given. The algorithm is similar to Nelson's algorithm since both involve the operations of complementing, expanding, and simplifying, but the new algorithm includes the additional operation of factoring. The algorithm with factoring is proved, and it is shown that factoring accounts for a dramatic increase in efficiency over Nelson's algorithm. The increased efficiency is illustrated with timing results obtained from several examples that were implemented for both algorithms using the symbolic manipulation systems SETS.

21 citations

References
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Journal ArticleDOI
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.
Abstract: A systematic procedure is presented for writing a Boolean function as a minimum sum of products This procedure is a simplification and extension of the method presented by W V Quine Specific attention is given to terms which can be included in the function solely for the designer's convenience

1,103 citations

Journal ArticleDOI
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.
Abstract: (1952). The Problem of Simplifying Truth Functions. The American Mathematical Monthly: Vol. 59, No. 8, pp. 521-531.

885 citations

Journal ArticleDOI
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.
Abstract: (1955). A Way to Simplify Truth Functions. The American Mathematical Monthly: Vol. 62, No. 9, pp. 627-631.

626 citations

Journal ArticleDOI
Maurice Karnaugh1
01 Nov 1953
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.
Abstract: THE SEARCH for simple abstract techniques to be applied to the design of switching systems is still, despite some recent advances, in its early stages The problem in this area which has been attacked most energetically is that of the synthesis of efficient combinational that is, nonsequential, logic circuits

610 citations


"Clause-Column Table Approach for Ge..." refers background or methods in this paper

  • ...Although there exists a good number of methods for determining the prime implicants of switching functions, the map methods of Veitch [1] and Karnaugh [3] and the tabular method of MIcCluskey [7], [21], that use the minterm form of switching functions, are the ones...

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  • ...[3] -, "On the computer classification of geometric line patterns," in Proc....

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