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Optimal Two-Level Boolean Minimization [chapter]

Robert P. Dick
2016 Encyclopedia of Algorithms  
The Quine-McCluskey method is used to permit efficient implementation of Boolean logic functions in a wide range of digital logic devices, including computers.  ...  The Quine-McCluskey method served as a starting point or inspiration for most currently used logic minimization algorithms.  ...  Boolean minimization is the task of deriving the tersest expression for a function.  ... 
doi:10.1007/978-1-4939-2864-4_446 fatcat:xkxy4fmw35dwjiyakzmt5nbhuu

Exact inference in multi-label CRFs with higher order cliques

Srikumar Ramalingam, Pushmeet Kohli, Karteek Alahari, Philip H. S. Torr
2008 2008 IEEE Conference on Computer Vision and Pattern Recognition  
We present a framework to transform special classes of multi-label higher order functions to submodular second order boolean functions (referred to as F 2 s ), which can be minimized exactly using graph  ...  We believe that our work on exact minimization of higher order energy functions will lead to similar improvements in solutions of other labelling problems.  ...  Acknowledgments This work was supported by the EPSRC research grants EP/C006631/1(P) and GR/T21790/01(P), the IST Programme of the European Community, under the PASCAL Network of Excellence, IST-2002-506778  ... 
doi:10.1109/cvpr.2008.4587401 dblp:conf/cvpr/RamalingamKAT08 fatcat:s7tlqgqvhfelzf67miiyxpnppm

Page 737 of Mathematical Reviews Vol. 34, Issue 3 [page]

1967 Mathematical Reviews  
In the second part of the paper the author derives expressions for (1) the minimal number of (normally open) contacts necessary for a planar, two terminal, realization of the symmetric Boolean function  ...  R. 261 (1965), 4297-4300 ; MR 33 #2481] on the minimal number of contacts necessary to realize such a function to derive necessary and sufficient conditions on the diagram of such a circuit in order that  ... 

Minimization of Multiple Value function using Quine Mc-Cluskey Technique

Prashant S., Gajanan Sarate
2016 International Journal of Computer Applications  
As the radix of system increases, the difficulties in the minimization or reduction of logic function is get increases.  ...  This paper provide steps for the minimization of multivalued function i.e. radix >2 digital system.  ...  For forming the decimal order, write order such that alembic sum of total no of variable is one under order one, repeat the procedure for decimal order till final order get obtained.  ... 
doi:10.5120/ijca2016910257 fatcat:p6k4t2gxhvetjlf2fyiwpl3x3u

Minimization of conjunctive normal forms of boolean functions by combinatorial method

Volodymyr Riznyk, Mykhailo Solomko
2018 Tehnologìčnij Audit ta Rezervi Virobnictva  
The transformation of the structure of a Boolean function in order to simplify the combinational device is called its minimization. Example 1.  ...  The regularity of variables of a Boolean function can be expressed by the degree of autosymmetry, which ultimately gives a new tool for effective minimization.  ...  It is established that the minimization of a CNF of the Boolean functions by the combinatorial method is based on a flowchart with a repetition. This is the truth table of this function.  ... 
doi:10.15587/2312-8372.2018.146312 fatcat:uuk6xqee6ncxplorhvw7sbrlda

Developing an algorithm to minimize boolean functions for the visual-matrix form of the analytical method

Mykhailo Solomko
2021 Eastern-European Journal of Enterprise Technologies  
This simplifies the procedure of searching for a minimal function. Compared to analogs, that makes it possible to improve the productivity of the Boolean function minimization process by 100‒200 %.  ...  This research has established the possibility of improving the effectiveness of the visual-matrix form of the analytical Boolean function minimization method by identifying reserves in a more complex algorithm  ...  (in a state of change) for theoretical research on the optimal Boolean function minimization.  ... 
doi:10.15587/1729-4061.2021.225325 fatcat:kscjnjb4qnadpdefyxx2rx2ota

Cause-effect relationships and partially defined Boolean functions

Yves Crama, Peter L. Hammer, Toshihide Ibaraki
1988 Annals of Operations Research  
This paper investigates the use of Boolean techniques in a systematic study of cause-effect relationships. The model uses partially defined Boolean functions.  ...  Procedures are provided to extrapolate from limited observations, concise and meaningful theories to explain the effect under study, and to prevent (or provoke) its occurrence.  ...  This research was initiated during visits of the first and third authors to RUTCOR, within the framework of the Discrete Applied Mathematics Project supported by the U.S.  ... 
doi:10.1007/bf02283750 fatcat:5bducfp7drg7nm3lnz5b62szua

Page 1260 of Mathematical Reviews Vol. , Issue 84c [page]

1984 Mathematical Reviews  
The main part of the paper deals with necessary conditions which must be satisfied by a Boolean function in order to be a Bent function.  ...  The problem of classifying third-degree Bent functions (up to affine equivalence) is discussed.  ... 

Truth Graph: A Novel Method for Minimizing Boolean Algebra Expressions by Using Graphs [chapter]

Eisa Alharbi
2020 Lecture Notes in Computer Science  
To reduce the cost and transaction numbers of logic circuits, engineers minimize Boolean expressions by reducing the number of terms or arithmetic operations.  ...  A well-known pictorial method applied for minimizing Boolean expressions is the Karnaugh map.  ...  The K-map is another form of the truth table that facilitates the minimization of Boolean algebra expressions without requiring the use of Boolean algebra theorems.  ... 
doi:10.1007/978-3-030-54249-8_36 fatcat:u65unpggfbhtlfcktk77counx4

Most complex Boolean functions detected by the specialized normal form

Bernd Steinbach
2007 Facta universitatis - series Electronics and Energetics  
It is well known that Exclusive Sum-Of-Products (ESOP) expressions for Boolean functions require on average the smallest number of cubes.  ...  The SNF is a unique (canonical) ESOP representation of a Boolean function. In this paper properties of the most complex Boolean functions are studied.  ...  Generally, the number of nodes of a BDD can be a complexity measure of the represented Boolean function, but this number depends on the chosen order of variables in the BDD.  ... 
doi:10.2298/fuee0703259s fatcat:3tfbmazb4vcmfi7ug2abbvmue4

Implementation of the method of figurative transformations to minimizing symmetric Boolean functions

Mykhailo Solomko, Petro Tadeyev, Liudmyla Zubyk, Stepaniia Babych, Yuliia Mala, Oksana Voitovych
2021 Eastern-European Journal of Enterprise Technologies  
This paper reports a study that has established the possibility of improving the effectiveness of the method of figurative transformations in order to minimize symmetrical Boolean functions in the main  ...  It was established that the simplification of symmetric Boolean functions by the method of figurative transformations is based on a flowchart with repetition, which is the actual truth table of the assigned  ...  When meditating on Tables 2, 3, we envision that the logical operation of the x x x x 1 2 1 2 + equivalence is a partial case on a set of similar equivalent transformations of Boolean expressions.  ... 
doi:10.15587/1729-4061.2021.239149 fatcat:mc3tgtufhvdwfhfd4jjbnelgfu

Quadratization and Roof Duality of Markov Logic Networks

Roderick Sebastiaan De Nijs, Christian Landsiedel, Dirk Wollherr, Martin Buss
2016 The Journal of Artificial Intelligence Research  
The procedure relies on a pseudo-Boolean representation of the model, and allows handling models of any order.  ...  Results on common benchmark problems show that the proposed approach finds optimal assignments for most variables in excellent computational time and approximate solutions that match the quality of ILP-based  ...  Study (, funded by the German Excellence Initiative.  ... 
doi:10.1613/jair.5023 fatcat:y6jk5vzr6fa6vfmp6vww2niv74

Optimal Boolean Function Simplification through K-Map using Object-Oriented Algorithm

Arunachalam Solairaju, Rajupillai Periyasamy
2011 International Journal of Computer Applications  
It is well known that the Karnaugh-map technique is an elegant teaching resource for academics and a systematic and powerful tool for a digital designer in minimizing low order Boolean functions.  ...  Why is the minimization of the Boolean expression needed? By simplifying the logic function, we can reduce the original number of digital components (gates) required to implement digital circuits.  ...  There may be a large number of boolean algebraic expressions that specify a given Boolean function.  ... 
doi:10.5120/1959-2621 fatcat:w3j3hsk3qjaunaoqoz65i2q6yu

A New Approach to Simplifying Boolean Functions

A. H. M. Ashfak Habib, Md. Abdus Salam, Zia Nadir, Hemen Goswami
2004 The Journal of Engineering Research  
But no method is effective for the simplification of Boolean functions, if it involves more than six variables.  ...  A reduced number of gates decreases considerably the cost of the hardware, reduces the heat generated by the chip and, most importantly, increases the speed.  ...  Conclusions This paper studied the problems of minimizing Boolean expressions and proposed an optimal method of Boolean function simplification. It also evaluated the performance of a new technique.  ... 
doi:10.24200/tjer.vol1iss1pp39-45 fatcat:f24jlcq32naedcnngg43jgvn2q

Application of super-sticking algebraic operation of variables for Boolean functions minimization by combinatorial method

Volodymyr Riznyk, Mykhailo Solomko
2017 Tehnologìčnij Audit ta Rezervi Virobnictva  
of a Boolean function reduces to the implementation of a single algebraic transformation. 5.3. 4-bit Boolean functions minimization.  ...  The proposed algorithm is the first one that gives a solution to the problem of finding minimum ESCT expressions for switching functions to six input variables.  ...  The protocol for Boolean function minimization of the combinatorial method is independent of the protocols of other minimization methods, so the threat of negative impact on the object of research of external  ... 
doi:10.15587/2312-8372.2017.118336 fatcat:mlojdcfnmvagvf53n7lbzsb64m
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