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Journal articles on the topic 'Boolean equation'

Author: Grafiati

Published: 5 June 2025

Last updated: 1 August 2025

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1

Allart, Emilie, Joachim Niehren, and Cristian Versari. "Exact Boolean Abstraction of Linear Equation Systems." Computation 9, no. 11 (2021): 113. http://dx.doi.org/10.3390/computation9110113.

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We study the problem of how to compute the boolean abstraction of the solution set of a linear equation system over the positive reals. We call a linear equation system ϕ exact for the boolean abstraction if the abstract interpretation of ϕ over the structure of booleans is equal to the boolean abstraction of the solution set of ϕ over the positive reals. Abstract interpretation over the booleans is thus complete for the boolean abstraction when restricted to exact linear equation systems, while it is not complete more generally. We present a new rewriting algorithm that makes linear equation

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2

Marovac, Ulfeta, and Dragic Bankovic. "Systems of k Boolean inequations and a Boolean equation." Filomat 34, no. 4 (2020): 1261–70. http://dx.doi.org/10.2298/fil2004261m.

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In this paper elementary generalized systems of Boolean equations are investigated. The formula for solving systems of k Boolean inequations and a Boolean equation is presented. This systems have many applications in computer science for solving logical problems. Presented formulas can accelerate application of elementary generalized systems of Boolean equations.

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3

Marovac, Ulfeta, and Dragic Bankovic. "Systems of k Boolean inequations and a Boolean equation." Filomat 34, no. 4 (2020): 1261–70. http://dx.doi.org/10.2298/fil2004261m.

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In this paper elementary generalized systems of Boolean equations are investigated. The formula for solving systems of k Boolean inequations and a Boolean equation is presented. This systems have many applications in computer science for solving logical problems. Presented formulas can accelerate application of elementary generalized systems of Boolean equations.

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4

Ali M. Ali Rushdi, Ali M. Ali Rushdi. "Satisfiability in Big Boolean Algebras via Boolean-Equation Solving." journal of King Abdulaziz University Engineering Sciences 28, no. 1 (2017): 3–18. http://dx.doi.org/10.4197/eng.28-1.1.

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This paper studies Satisfiability (SAT) in finite atomic Boolean algebras larger than the two-valued one B2, which are named big Boolean algebras. Unlike the formula ݃(ࢄ (in the SAT problem over B2, which is either satisfiable or unsatisfiable, this formula for the SAT problem over a big Boolean algebra could be unconditionally satisfiable, conditionally satisfiable, or unsatisfiable depending on the nature of the consistency condition of the Boolean equation {݃(ࢄ = (1}, since this condition could be an identity, a genuine equation, or a contradiction. The paper handles this latter SAT problem

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5

Steinbach, Bernd, and Christian Posthoff. "Boolean differential equations: A common model for classes, lattices, and arbitrary sets of Boolean functions." Facta universitatis - series: Electronics and Energetics 28, no. 1 (2015): 51–76. http://dx.doi.org/10.2298/fuee1501051s.

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The Boolean Differential Calculus (BDC) significantly extends the Boolean Algebra because not only Boolean values 0 and 1, but also changes of Boolean values or Boolean functions can be described. A Boolean Differential Equation (BDe) is a Boolean equation that includes derivative operations of the Boolean Differential Calculus. This paper aims at the classification of BDEs, the characterization of the respective solutions, algorithms to calculate the solution of a BDe, and selected applications. We will show that not only classes and arbitrary sets of Boolean functions but also lattices of Bo

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6

Rudeanu, Sergiu. "On the Decomposition of Boolean Functions via Boolean Equations." JUCS - Journal of Universal Computer Science 10, no. (9) (2004): 1294–301. https://doi.org/10.3217/jucs-010-09-1294.

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We propose an alternative solution to the problems solved in [1]. Our aim is to advocate the efficiency of algebraic methods for the solution of the Boolean equations which occur in the decomposition of Boolean functions.

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7

Balamesh, Ahmed S., and Ali M. Rushdi. "Atomic Formulation of the Boolean Curve Fitting Problem." International Journal of Mathematical, Engineering and Management Sciences 7, no. 5 (2022): 670–780. http://dx.doi.org/10.33889/ijmems.2022.7.5.044.

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Boolean curve fitting is the process of finding a Boolean function that takes given values at certain points in its Boolean domain. The problem boils down to solving a set of ‘big’ Boolean equations that may or may not be consistent. The usual formulation of the Boolean curve fitting problem is quite complicated, indeed. In this paper, we formulate the Boolean curve fitting problem using the technique of atomic decomposition of Boolean equations. This converts the problem into a set of independent switching equations. We present the solution of these switching equations and express the solutio

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8

Li, Xiang, Hanxiang Shen, Weiguo Gao, and Yingzhou Li. "Resource Efficient Boolean Function Solver on Quantum Computer." Quantum 8 (October 10, 2024): 1500. http://dx.doi.org/10.22331/q-2024-10-10-1500.

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Nonlinear boolean equation systems play an important role in a wide range of applications. Grover&apos;s algorithm is one of the best-known quantum search algorithms in solving the nonlinear boolean equation system on quantum computers. In this paper, we propose three novel techniques to improve the efficiency under Grover&apos;s algorithm framework. A W-cycle circuit construction introduces a recursive idea to increase the solvable number of boolean equations given a fixed number of qubits. Then, a greedy compression technique is proposed to reduce the oracle circuit depth. Finally, a

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9

Rushdi, Ali Muhammad Ali, and Waleed Ahmad. "Digital Circuit Design Utilizing Equation Solving over ‘Big’ Boolean Algebras." International Journal of Mathematical, Engineering and Management Sciences 3, no. 4 (2018): 404–28. http://dx.doi.org/10.33889/ijmems.2018.3.4-029.

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A task frequently encountered in digital circuit design is the solution of a two-valued Boolean equation of the form h(X,Y,Z)=1, where h: B_2^(k+m+n)→ B_2 and X,Y, and Z are binary vectors of lengths k, m, and n, representing inputs, intermediary values, and outputs, respectively. The resultant of the suppression of the variables Y from this equation could be written in the form g(X,Z)=1 where g: B_2^(k+n)→ B_2. Typically, one needs to solve for Z in terms of X, and hence it is unavoidable to resort to ‘big’ Boolean algebras which are finite (atomic) Boolean algebras larger than the two-valued

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10

Groote, Jan Friso, and Tim A. C. Willemse. "Parameterised boolean equation systems." Theoretical Computer Science 343, no. 3 (2005): 332–69. http://dx.doi.org/10.1016/j.tcs.2005.06.016.

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11

Peryazev, N. A. "Systems of Inclusions with Unknowns in Multioperations." Bulletin of Irkutsk State University. Series Mathematics 38 (2021): 112–23. http://dx.doi.org/10.26516/1997-7670.2021.38.112.

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We consider systems of inclusions with unknowns and coefficients in multioperations of finite rank. An algorithm for solving such systems by the method of reduction to Boolean equations using superposition representation of multioperations by Boolean space matrices is given. Two methods for solving Boolean equations with many unknowns are described for completeness. The presentation is demonstrated by examples: the representation of the superposition of multioperations by Boolean space matrices; solving a Boolean equation by analytical and numerical methods; and finding solutions to an inclusi

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12

Liu, Hui, Fukun Li, and Yilin Fan. "Optimizing the Quantum Circuit for Solving Boolean Equations Based on Grover Search Algorithm." Electronics 11, no. 15 (2022): 2467. http://dx.doi.org/10.3390/electronics11152467.

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The solution of nonlinear Boolean equations in a binary field plays a crucial part in cryptanalysis and computational mathematics. To speed up the process of solving Boolean equations is an urgent task that needs to be addressed. In this paper, we propose a method for solving Boolean equations based on the Grover algorithm combined with preprocessing using classical algorithms, optimizing the quantum circuit for solving the equations, and implementing the automatic generation of quantum circuits. The method first converted Boolean equations into Boolean expressions to construct the oracle in t

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13

Ali, Muhammad Ali Rushdi, and Ahmad Waleed. "A Novel Method for Compact Listing of All Particular Solutions of a System of Boolean Equations." British Journal of Mathematics & Computer Science 22, no. 6 (2017): 1–18. https://doi.org/10.9734/BJMCS/2017/33884.

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Any system of ‘big’ Boolean equations can be reduced to a single Boolean equation . We propose a novel method for producing a general parametric solution for such a Boolean equation without attempting to minimize the number of parameters used, but instead using independent parameters belonging to the two-valued Boolean algebra B2 for each asserted atom that appears in the discriminants of the function . We sacrifice minimality of parameters and algebraic expressions for ease, compactness and efficiency in listing all particular solutions. These solutions are given by additive formulas expressi

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14

HERLIHY, BRIAN, PETER SCHACHTE, and HARALD SØNDERGAARD. "UN-KLEENE BOOLEAN EQUATION SOLVING." International Journal of Foundations of Computer Science 18, no. 02 (2007): 227–50. http://dx.doi.org/10.1142/s0129054107004668.

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We present a new method for finding closed forms of recursive Boolean function definitions. Traditionally, these closed forms are found by Kleene iteration: iterative approximation until a fixed point is reached. Conceptually, our new method replaces each k-ary function by 2k Boolean constants defined by mutual recursion. The introduction of an exponential number of constants is mitigated by the simplicity of their definitions and by the use of a novel variant of ROBDDs to avoid repeated computation. Experiments suggest that this approach is significantly faster than Kleene iteration for examp

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15

Hao, Cao, Shi Min Wei, and Hui Ge Wang. "Algorithms of Constructing Symmetric Boolean Functions with Second-Order Correlation-Immunity." Applied Mechanics and Materials 411-414 (September 2013): 67–71. http://dx.doi.org/10.4028/www.scientific.net/amm.411-414.67.

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Constructing n-variable symmetric Boolean Functions with Second-Order Correlation-Immunity is equivalent to solving the equation in the binary field. By discussing the relationships between the solutions of the equation, and using the characteristics of the equation and its equivalent equation, algorithms of constructing symmetric Boolean Functions with Second-Order Correlation-Immunity is proposed.

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16

Yeghiazaryan, Ed V. "ASYMPTOTIC ESTIMATES OF THE NUMBER OF SOLUTIONS OF SYSTEMS OF EQUATIONS WITH DETERMINABLE PARTIAL BOOLEAN FUNCTIONS." Proceedings of the YSU A: Physical and Mathematical Sciences 53, no. 2 (249) (2019): 127–31. http://dx.doi.org/10.46991/pysu:a/2019.53.2.127.

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In this paper we investigate a class of equation systems with determinable partial (not everywhere defined) Boolean functions. We found the asymptotic estimate of the number of solutions of equation systems in the “typical” case (for the whole range of changes in the number of equations).

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17

Orzan, Simona, and Tim A. C. Willemse. "Invariants for Parameterised Boolean Equation Systems." Theoretical Computer Science 411, no. 11-13 (2010): 1338–71. http://dx.doi.org/10.1016/j.tcs.2009.11.001.

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18

Keiren, Jeroen J. A., Michel A. Reniers, and Tim A. C. Willemse. "Structural Analysis of Boolean Equation Systems." ACM Transactions on Computational Logic 13, no. 1 (2012): 1–35. http://dx.doi.org/10.1145/2071368.2071376.

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19

Wang, Guo Ping, Hua Ling Chen, She Miao Qi, and Lie Yu. "Key Problem of Solving Nonlinear Reynolds Equation." Applied Mechanics and Materials 241-244 (December 2012): 2751–57. http://dx.doi.org/10.4028/www.scientific.net/amm.241-244.2751.

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Finite element equation of the nonlinear dimensionless Reynolds equation, based on the Galerkin finite element method, was derived. Three key points of solving the equation was studied in detail, i.e. Boolean matrix was calculated under the nonlinear conditions, and a method of integrating discrete element equations was provided; Nonlinear algebraic equations set, resulted from integrated finite element equations, was obtained and a method how to substitute boundary conditions into the algebraic equations was presented; A method of calculating the Jacobi matrix of the equations set were descri

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20

Pakhomchik, Aleksey I., Vladimir V. Voloshinov, Valerii M. Vinokur, and Gordey B. Lesovik. "Converting of Boolean Expression to Linear Equations, Inequalities and QUBO Penalties for Cryptanalysis." Algorithms 15, no. 2 (2022): 33. http://dx.doi.org/10.3390/a15020033.

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There exists a wide range of constraint programming (CP) problems defined on Boolean functions depending on binary variables. One of the approaches to solving CP problems is using specific appropriate solvers, e.g., SAT solvers. An alternative is using the generic solvers for mixed-integer linear programming problems (MILP), but they require transforming expressions with Boolean functions to linear equations or inequalities. Here, we present two methods of such a transformation which applies to any Boolean function defined by explicit rules giving values of the Boolean function for all combina

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21

Das, Haimabati, and Ritwik Kumar Layek. "Estimation of delays in generalized asynchronous Boolean networks." Molecular BioSystems 12, no. 10 (2016): 3098–110. http://dx.doi.org/10.1039/c6mb00276e.

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The generalized asynchronous Boolean network model proposed in this paper can reliably mimic the temporal behavior of the Ordinary Differential Equation model without compromising the flexibility of the Boolean network model.

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22

Mardanov, Sahib S., and Knyaz Sh Mamedov. "Disaggregation of Diophantine Equation with Boolean Variables." Computational Optimization and Applications 27, no. 1 (2004): 31–36. http://dx.doi.org/10.1023/b:coap.0000004978.46548.d8.

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23

Tsaregorodtsev, Kirill D. "Properties of proper families of Boolean functions." Discrete Mathematics and Applications 32, no. 5 (2022): 369–78. http://dx.doi.org/10.1515/dma-2022-0030.

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Abstract We show that triangular families of Boolean functions comprise an exponentially small fraction of proper families of a given order. We prove that if F is a proper family of Boolean functions, then the number of solutions of an equation F(x) = A is even. Finally, we describe a new class of proper families of Boolean functions.

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24

Rushdi, Ali Muhammad Ali, and Adnan Ahmad Alsogati. "Matrix Analysis of Synchronous Boolean Networks." International Journal of Mathematical, Engineering and Management Sciences 6, no. 2 (2021): 598–610. http://dx.doi.org/10.33889/ijmems.2021.6.2.036.

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The synchronous Boolean network (SBN) is a simple and powerful model for describing, analyzing, and simulating cellular biological networks. This paper seeks a complete understanding of the dynamics of such a model by employing a matrix method that relies on relating the network transition matrix to its function matrix via a self-inverse state matrix. A recursive ordering of the underlying basis vector leads to a simple recursive expression of this state matrix. Hence, the transition matrix is computed via multiplication of binary matrices over the simplest finite (Galois) field, namely the bi

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25

Lytvynenko, Olexander. "METHOD OF SOLVING NONLINEAR EQUATION SYSTEMS WITH BOOLEAN VARIABLES." Aviation 12, no. 3 (2008): 80–86. http://dx.doi.org/10.3846/1648-7788.2008.12.80-86.

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A method of solving nonlinear equation systems with Boolean variables, which realizes the strategy of variant‐directed enumeration, is related. Necessary and sufficient conditions of feasible plans existence are formalized. A procedure for the formal analysis of subsets of the variants is described. The structure of the algorithm that possesses the completeness property is given. Special cases of systems of equations are considered. Santrauka Netiesinių lygčių sistemos su Būlio kintamaisiais sprendžiamos naudojant variantų kryptinės numeracijos metodą. Formalizuojamos būtinos ir pakankamos gal

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26

Reniers, Michel A., and Tim A. C. Willemse. "Analysis of Boolean Equation Systems through Structure Graphs." Electronic Proceedings in Theoretical Computer Science 18 (February 15, 2010): 92–107. http://dx.doi.org/10.4204/eptcs.18.7.

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27

Saunders, Amira, and Michael Ghil. "A Boolean delay equation model of ENSO variability." Physica D: Nonlinear Phenomena 160, no. 1-2 (2001): 54–78. http://dx.doi.org/10.1016/s0167-2789(01)00331-1.

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28

Keinänen, Misa. "Obtaining Memory-Efficient Solutions to Boolean Equation Systems." Electronic Notes in Theoretical Computer Science 133 (May 2005): 175–91. http://dx.doi.org/10.1016/j.entcs.2004.08.064.

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29

Barotov, D. N. "Criteria for satisfiability and monotonicity of a Boolean function in terms of its polylinear continuation." Mathematical structures and modeling, no. 2 (2024): 5–12. http://dx.doi.org/10.24147/2222-8772.2024.2.5-12.

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This paper examines the criteria for the satisfiability and monotonicity of a Boolean function in terms of its polylinear continuation, namely, firstly, a necessary and sufficient condition for the monotonicity of a Boolean function in terms of its polylinear continuation is found, and secondly, proved that by only once calculating the value of the polylinear continuation 𝑝𝐷(𝑥1, 𝑥2, ..., 𝑥𝑛) of the Boolean function 𝑝(𝑥1, 𝑥2, ..., 𝑥𝑛) at any interior point of the unit 𝑛-dimensional cube [0, 1]𝑛, we can determine the satisfiability of the Boolean function 𝑝(𝑥1, 𝑥2, ..., 𝑥𝑛) and, in the central a

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30

Nichita, Florin F. "Unification Theories: Rings, Boolean Algebras and Yang–Baxter Systems." Axioms 12, no. 4 (2023): 341. http://dx.doi.org/10.3390/axioms12040341.

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This paper continues a series of papers on unification constructions. After a short discussion on the Euler’s relation, we introduce a matrix version of the Euler’s relation, E I π+U=O. We refer to a related equation, the Yang–Baxter equation, and to Yang–Baxter systems. The most consistent part of the paper is on the unification of rings and Boolean algebras. These new structures are related to the Yang–Baxter equation and to Yang–Baxter systems.

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31

Schilling, Thorsten, and Pavol Zajac. "Phase transition in a system of random sparse Boolean equations." Tatra Mountains Mathematical Publications 45, no. 1 (2010): 93–105. http://dx.doi.org/10.2478/v10127-010-0008-7.

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ABSTRACT Many problems, including algebraic cryptanalysis, can be transformed to a problem of solving a (large) system of sparse Boolean equations. In this article we study 2 algorithms that can be used to remove some redundancy from such a system: Agreeing, and Syllogism method. Combined with appropriate guessing strategies, these methods can be used to solve the whole system of equations. We show that a phase transition occurs in the initial reduction of the randomly generated system of equations. When the number of (partial) solutions in each equation of the system is binomially distributed

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32

GROOTE, JAN FRISO, and BAS PLOEGER. "SWITCHING GRAPHS." International Journal of Foundations of Computer Science 20, no. 05 (2009): 869–86. http://dx.doi.org/10.1142/s0129054109006930.

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Switching graphs are graphs that contain switches. A switch is a pair of edges that start in the same vertex and of which precisely one edge is enabled at any time. By using a Boolean function called a switch setting, the switches in a switching graph can be put in a fixed direction to obtain an ordinary graph. For many problems, switching graphs are a remarkable straightforward and natural model, but they have hardly been studied. We study the complexity of several natural questions in switching graphs of which some are polynomial, and others are NP-complete. We started investigating switchin

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33

Mvondo, Esther Claudine Bitye. "Computational Resolution of a Boolean Equation of 21 Variables." American Journal of Operations Research 12, no. 05 (2022): 157–78. http://dx.doi.org/10.4236/ajor.2022.125009.

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34

Nagae, Yutaro, and Masahiko Sakai. "Reduced Dependency Spaces for Existential Parameterised Boolean Equation Systems." Electronic Proceedings in Theoretical Computer Science 265 (February 16, 2018): 67–81. http://dx.doi.org/10.4204/eptcs.265.6.

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35

Serfati, Michel. "A Note on Postian Matrix Theory." International Journal of Algebra and Computation 07, no. 02 (1997): 161–79. http://dx.doi.org/10.1142/s0218196797000101.

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The present paper is devoted to some aspects of postian matrix theory over an arbitrary Post algebra, through results in Postian relative–pseudocomplementation. It is well known (for instance Rousseau [10] or Dwinger [6]) that any r-Post algebra is a Brouwerian lattice (or a Heyting algebra), that is to say, for every (a, b) in P2, the set of x in P such as a. x ≤ b admits a greatest element (a.x is inf {a, x}), called the relative inf–pseudocomplement of a in b, and denoted (b|a). In the first part of our paper, we compute the explicit expression of the disjunctive components of the relative

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36

Zhao, Ying Ding, and Xian Xia Qiao. "Review of Modeling Methods of Gene Expression Regulation Networks." Applied Mechanics and Materials 433-435 (October 2013): 783–87. http://dx.doi.org/10.4028/www.scientific.net/amm.433-435.783.

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the study of Gene expression regulation network is expected to fully disclose function and behavior of the genome from the perspective of system. Now, Gene expression regulation network construction methods include Boolean networks, linear combination, the weighted matrix, Bayesian networks and differential equation, And so on, These methods are real abstraction of gene expression regulation network at different levels. Boolean network is qualitative research network of gene expression regulating, And Differential equation is quantified to describe biological processes by detailed mathematical

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37

Resconi, Germano. "Boolean Models Guide Intentionally Continuous Information and Computation Inside the Brain." Oriental journal of computer science and technology 12, Issue 3 (2019): 90–98. http://dx.doi.org/10.13005/ojcst12.03.03.

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In 1943 Machculloch and Pitts create the formal neuron where many input signals are linearly composed with different weights on the neuron soma. When the soma electrical signal goes over a specific threshold an output is produced. The main topic in this model is that the response is the same response as in a Boolean function used a lot for the digital computer. Logic functions can be simplified with the formal neuron. But there is the big problem for which not all logic functions, as XOR , cannot be designed in the formal neuron. After a long time the back propagation and many other neural mod

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38

Can, Yavuz. "Disjointed sum of products by a novel technique of orthogonalizing ORing." Open Mathematics 16, no. 1 (2018): 392–406. http://dx.doi.org/10.1515/math-2018-0038.

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AbstractThis work presents a novel combining method called ‘orthogonalizing ORing $\bigcirc\!\!\!\!\!\!\vee $’ which enables the building of the union of two conjunctions whereby the result consists of disjointed conjunctions. The advantage of this novel technique is that the results are already presented in an orthogonal form which has a significant advantage for further calculations as the Boolean Differential Calculus. By orthogonalizing ORing two calculation steps - building the disjunction and the subsequent orthogonalization of two conjunctions - are performed in one step. Postulates, ax

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Kant, Gijs, and Jaco van de Pol. "Efficient Instantiation of Parameterised Boolean Equation Systems to Parity Games." Electronic Proceedings in Theoretical Computer Science 99 (October 23, 2012): 50–65. http://dx.doi.org/10.4204/eptcs.99.7.

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40

Neele, Thomas, Tim A. C. Willemse, and Jan Friso Groote. "Finding compact proofs for infinite-data parameterised Boolean equation systems." Science of Computer Programming 188 (March 2020): 102389. http://dx.doi.org/10.1016/j.scico.2019.102389.

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41

Kalkan, Tugce, Florin F. Nichita, Tahsin Oner, Ibrahim Senturk, and Mehmet Terziler. "Mathematics and Poetry · Yang–Baxter Equations, Boolean Algebras, and BCK-Algebras." Sci 4, no. 2 (2022): 16. http://dx.doi.org/10.3390/sci4020016.

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The current paper explores the potential of the areas between mathematics and poetry. We will first recall some definitions and results that are needed to construct solutions of the Yang–Baxter equation. A new duality principle is presented and Boolean coalgebras are introduced. A section on poetry dedicated to the Yang–Baxter equation is presented, and a discussion on a poem related to a mathematical formula follows. The final section presents our conclusions and further information on these topics.

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42

Aziz, Elham. "Design Simulation System to Simplifying Boolean Equation by using Karnaugh Map." AL-Rafidain Journal of Computer Sciences and Mathematics 14, no. 1 (2020): 113–31. http://dx.doi.org/10.33899/csmj.2020.164680.

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Nagae, Yutaro, Masahiko Sakai, and Hiroyuki Seki. "An Extension of Proof Graphs for Disjunctive Parameterised Boolean Equation Systems." Electronic Proceedings in Theoretical Computer Science 235 (January 1, 2017): 46–61. http://dx.doi.org/10.4204/eptcs.235.4.

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44

Ploeger, B., J. W. Wesselink, and T. A. C. Willemse. "Verification of reactive systems via instantiation of Parameterised Boolean Equation Systems." Information and Computation 209, no. 4 (2011): 637–63. http://dx.doi.org/10.1016/j.ic.2010.11.025.

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45

Darby, M. S., and L. A. Mysak. "A Boolean delay equation model of an interdecadal Arctic climate cycle." Climate Dynamics 8, no. 5 (1993): 241–46. http://dx.doi.org/10.1007/bf00198618.

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46

JOY, MALIACKAL POULO, DONALD E. INGBER, and SUI HUANG. "CHAOTIC MEAN FIELD DYNAMICS OF A BOOLEAN NETWORK WITH RANDOM CONNECTIVITY." International Journal of Modern Physics C 18, no. 09 (2007): 1459–73. http://dx.doi.org/10.1142/s0129183107011467.

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Random Boolean networks have been used as simple models of gene regulatory networks, enabling the study of the dynamic behavior of complex biological systems. However, analytical treatment has been difficult because of the structural heterogeneity and the vast state space of these networks. Here we used mean field approximations to analyze the dynamics of a class of Boolean networks in which nodes have random degree (connectivity) distributions, characterized by the mean degree k and variance D. To achieve this we generalized the simple cellular automata rule 126 and used it as the Boolean fun

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47

Ali Muhammad Rushdi, Ali Muhammad Rushdi. "Two Novel Characterizations of the DE Flip Flop." journal of King Abdulaziz University Engineering Sciences 30, no. 1 (2018): 3–18. http://dx.doi.org/10.4197/eng.30-1.1.

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Modern digital circuits, especially those based on large-scale integration devices employ DE flip flops, which are an extension of the D type with the capacity to store an input value only upon request or enabling. The DE flip flop could possibly be described algebraically by its characteristic equation or tabularly by its next-state table (used for analysis purposes) and its excitation table (used for synthesis purposes). This paper explores two novel characterizations of DE flip flops. First, equational and implicational descriptions are presented, and the Modern Syllogistic Method is utiliz

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Nikonov, V. G., and A. N. Shurupov. "Threshold interpolations in solving nonlinear boolean equation by method of separating planes." Prikladnaya diskretnaya matematika. Prilozhenie, no. 10 (September 1, 2017): 165–68. http://dx.doi.org/10.17223/2226308x/10/64.

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JAFARI, MOHSEN A., GLENN A. MEREDITH, and THOMAS O. BOUCHER. "A transformation from a Boolean equation control specification to a Petri net." IIE Transactions 27, no. 1 (1995): 9–22. http://dx.doi.org/10.1080/07408179508936713.

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Crama, Y., P. L. Hammer, B. Jaumard, and B. Simeone. "Product form parametric representation of the solutions to a quadratic boolean equation." RAIRO - Operations Research 21, no. 4 (1987): 287–305. http://dx.doi.org/10.1051/ro/1987210402871.

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