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Algorithms Using First-Order Neighborhoods for minimization of boolean functions

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS 2013年第9期53卷 1410-1420页

作者： Panov, A. V. Moscow MV Lomonosov State Univ Fac Computat Math & Cybernet Moscow 119991 Russia

A class of minimization algorithms for boolean functions that involve conjunctions from a reduced disjunctive normal form and first-order neighborhoods of such conjunctions is investigated. A particular algorithm is s... 详细信息

关键词： minimization of boolean functions local algorithms information-computing algorithms majorant algorithms

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minimization of boolean functions Which Include Don't-Care Statements, Using Graph Data Structure

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3rd International Conference on Wireless, Mobile Networks, and Applications/1st International Conference on Computer Science, Engineering and Applications

作者： Nosrati, Masoud Karimi, Ronak Aziztabar, Reza Islamic Azad Univ Kermanshah Branch Kermanshah Iran Qom Univ Dept Informat Technol Qom Iran

ISBN: (纸本)9783642211522

In this paper, we intend to introduce a heuristic algorithm to apply maximum minimization to boolean functions with normal SOP form. To implement the proposed algorithm, we use the graph data structure and define the adjacencies. Also, we demonstrate some conditions to achieve the maximum minimization. Through this paper, the problem of shared vertices in more than one adjacency is talked, and the solution is presented. Also, don't-care statements are considered and the way of behaving with them is explained. Karnaugh map is used to clarify the matter.

关键词： minimization of boolean functions SOP form Don't-care statements Graph data structure

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Application of Hypergraphs in the Prime Implicants Selection Process 13

Application of Hypergraphs in the Prime Implicants Selection...

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13th IFAC and IEEE Conference on Programmable Devices and Embedded Systems

作者： Wisniewski, R. Stefanowicz, L. Bazydlo, G. Wegrzyn, M. Univ Zielona Gora Inst Comp Engn & Elect Zielona Gora Poland Univ Zielona Gora Fac Elect Engn Comp Sci & Telecommun Zielona Gora Poland

The paper presents a new concept of the selection of prime implicants in a two-level logic minimization of boolean functions. The method is based on the two-level minimization process of the boolean functions, according to the Quine-McCluskey approach. Initially, the set of prime implicants for the logic function ought to be calculated. Next, the selection process is applied to achieve the minimal formula. Such an operation is a typical covering problem and in general case it has exponential computational complexity. In the paper we propose a new prime implicants selection method. An idea is based on the hypergraph theory. The prime implicants matrix (chart) is formed as a selection hypergraph. If the selection hyper-graph belongs to the Exact Transversal Hypergraph class (xt-doss), the solution may be obtained in a polynomial time, which is not possible in a general case. The proposed method is illustrated by an example All necessary steps will be shown in order to apply the proposed selection algorithm to minimize an exemplary boolean function. (C) 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： minimization of boolean functions selection of prime implicants hypergraph exact transversal

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Application of Hypergraphs in the Prime Implicants Selection Process

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IFAC-PapersOnLine 2015年第4期48卷 302-305页

作者： R. Wiśniewski Ł. Stefanowicz G. Bazydło M. Węgrzyn University of Zielona Góra Institute of Computer Engineering and Electronics Zielona Góra Poland University of Zielona Góra Faculty of Electrical Engineering Computer Science and Telecommunication Zielona Góra Poland

The paper presents a new concept of the selection of prime implicants in a two-level logic minimization of boolean functions. The method is based on the two-level minimization process of the boolean functions, according to the Quine-McCluskey approach. Initially, the set of prime implicants for the logic function ought to be calculated. Next, the selection process is applied to achieve the minimal formula. Such an operation is a typical covering problem and in general case it has exponential computational complexity. In the paper we propose a new prime implicants selection method. An idea is based on the hypergraph theory. The prime implicants matrix (chart) is formed as a selection hypergraph. If the selection hyper-graph belongs to the Exact Transversal Hypergraph class ( xt-class ), the solution may be obtained in a polynomial time, which is not possible in a general case. The proposed method is illustrated by an example. All necessary steps will be shown in order to apply the proposed selection algorithm to minimize an exemplary boolean function.

关键词： minimization of boolean functions selection of prime implicants hypergraph exact transversal

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Operations on binary images encoded as minimized boolean functions

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PATTERN RECOGNITION LETTERS 1997年第5期18卷 455-463页

作者： Sarkar, D Variable Energy Cyclotron Centre 1/AF Bidhan Nagar Calcutta 700 064 India

A novel scheme has been devised to represent binary images as minimized boolean functions. The blocks corresponding to the essential prime implicants are stored as ternary numbers. The scheme has been shown to be simple and very much storage-saving. Based on this new scheme, the present paper describes the formula, computational techniques and algorithms of various set operations (viz. intersection, union, complement) and geometric operations (viz. area and centroid) on binary images. The computational complexities of the algorithms are also discussed. (C) 1997 Published by Elsevier Science B.V.

关键词： encoding of binary image minimization of boolean functions set operations geometric operations

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boolean function-based approach for encoding of binary images

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PATTERN RECOGNITION LETTERS 1996年第8期17卷 839-848页

作者： Sarkar, D Variable Energy Cyclotron Centre 1/AF Bidhan Nagar Calcutta 700 064 India

A scheme for representing binary images, based on minimization of boolean functions is introduced. The binary image is considered as a map of boolean function and the Quine-McCluskey method is applied to minimize the function. The terms of the minimized function represent the image. Drastic saving of storage is achieved compared to linear quadtrees and interpolation-based bintrees. Properties of the code are also discussed. Experiment shows that the number of codes required to represent a binary image by the proposed method is about 40% of that by the linear quadtree method and 55 to 60% of that by the interpolation-based bintree method.

关键词： encoding of binary image minimization of boolean functions

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boolean DERIVATIVES AND COMPUTATION OF CELLULAR AUTOMATA

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International Journal of Modern Physics C 1992年第2期3卷 307-320页

作者： FRANCO BAGNOLI Dipartimento di Matematica Applicata Università di Firenze Firenze I 50139 Italy

The derivatives of a boolean function are defined up to any order. The Taylor and MacLaurin expansions of a boolean function are thus obtained. The last corresponds to the ring sum expansion (RSE) of a boolean function, and is a more compact form than the usual canonical disjunctive form. For totalistic functions the RSE allows the saving of a large number of boolean operations. The algorithm has natural applications to the simulations of cellular automata using the multi-site coding technique. Several already published algorithms are analyzed, and expressions with fewer terms are generally found.

关键词： boolean Derivatives Cellular Automata minimization of boolean functions Multi-site Technique

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PROJECTION OF A BINARY CRITERION INTO A MODEL OF HIERARCHICAL CLASSES

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PSYCHOMETRIKA 1990年第4期55卷 677-694页

作者： VANMECHELEN, I DEBOECK, P CATHOLIC UNIV LEUVEN DEPT PSYCHOLTIENSESTR 102B-3000 LOUVAINBELGIUM

A formal analysis is made of how project an attribute criterion into the hierarchical classes model for object by attribute data proposed by De Boeck and Rosenberg. The projection is conceptualized as the prediction of the attribute criterion by means of a logical rule defined on the basis of attribute combinations from the model. Eliminative and constructive strategies are proposed to find logical rules with maximal predictive power and minimal formula complexity. Logical analyses of a real data set are reported and compared with a logistic regression to demonstrate the usefulness of the logical strategies, and to show the complementarity of logical and probabilistic approaches.

关键词： HIERARCHICAL CLASSES LOGICAL COMBINATIONS minimization of boolean functions

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A New Technique for the Fast minimization of Switching functions

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IEEE Transactions on Computers 1977年第8期C-26卷 757-764页

作者： Rhyne, V. Thomas Noe, Philip S. McKinney, Melvin H. Pooch, Udo W. Department of Electrical Engineering Texas A&M University College Station TX 77843 United States Department of Computer Science University Southwest Louisiana Lafayette LA 70501 United States Department of Industrial Engineering Texas A&M University College Station TX 77843 United States

The minimization of switching functions involving many variables is a difficult task. This paper presents a new minimization procedure that allows this process to be implemented with reduced computational effort. This procedure, designated as the directed-search algorithm, is applicable to both manual and computer-programmed minimization. The details of the algorithm are presented and illustrated by example. Comparative run-times between another minimization program and the directed-search algorithm, as implemented in Fortran, are also given. Copyright © 1977 by The Institute of Electrical and Electronics Engineers, Inc.

关键词： minimization of boolean functions prime implicants row dominance search tree switching algebra

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