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Journal articles on the topic 'Boolean-equation solving'

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Published: 3 June 2025

Last updated: 31 July 2025

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1

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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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

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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6

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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7

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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8

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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9

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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10

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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11

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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12

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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13

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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14

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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15

Noskov, Sergey I., and Anton N. Shakhurov. "Maximizing the number of allowable approximation errors when building a linear regression model." Yugra State University Bulletin 20, no. 3 (2024): 57–62. http://dx.doi.org/10.18822/byusu20240357-62.

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Subject of research: errors in approximation of a linear regression model within the framework of a logical-algebraic approach to data analysis. Purpose of the study: to develop an algorithmic method for solving the problem of maximizing the number of permissible approximation errors using a linear-Boolean programming computer. Methods and objects of research: the object of research is a linear regression model, the methods are linear regression analysis and mathematical programming apparatus. Main results of the study: an algorithmic method is proposed for maximizing the number of permissible

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16

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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17

Sun, Zhong, Giacomo Pedretti, Elia Ambrosi, Alessandro Bricalli, Wei Wang, and Daniele Ielmini. "Solving matrix equations in one step with cross-point resistive arrays." Proceedings of the National Academy of Sciences 116, no. 10 (2019): 4123–28. http://dx.doi.org/10.1073/pnas.1815682116.

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Conventional digital computers can execute advanced operations by a sequence of elementary Boolean functions of 2 or more bits. As a result, complicated tasks such as solving a linear system or solving a differential equation require a large number of computing steps and an extensive use of memory units to store individual bits. To accelerate the execution of such advanced tasks, in-memory computing with resistive memories provides a promising avenue, thanks to analog data storage and physical computation in the memory. Here, we show that a cross-point array of resistive memory devices can dir

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18

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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19

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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20

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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21

Raskin, Lev, Viacheslav Karpenko, Yuriy Ivanchykhin, and Dmytro Sokolov. "DIAGNOSIS OF SYSTEMS UNDER CONDITIONS OF SMALL INITIAL DATA SAMPLING." Advanced Information Systems 7, no. 3 (2023): 39–43. http://dx.doi.org/10.20998/2522-9052.2023.3.05.

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Object of the study is to assess systems state in conditions of a small sample of initial data. Relevance of the problem is as follows. The functioning of a significant number of real objects takes place under conditions of poorly predicted changes in the values of environmental factors affecting system efficiency. The resulting heterogeneity of the results of objects experimental study and the environment of their functioning leads to reduction in sample size. At the same time, the standard requirements regarding the correspondence of the number of experiments and the number of coefficients o

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22

Rushdi, Ali Muhammad Ali, and Waleed Ahmad. "A Comparison of the Methods of Boolean-Equation Solving and Input-Domain Constraining for Handling Type-2 Problems of Digital Circuit Design." Current Journal of Applied Science and Technology 29, no. 2 (2018): 1–15. http://dx.doi.org/10.9734/cjast/2018/43728.

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23

Noskov, Sergey I. "CONSTRUCTION OF EXPERT-STATISTICAL MODELS FROM INCOMPLETE DATA." T-Comm 15, no. 6 (2021): 33–39. http://dx.doi.org/10.36724/2072-8735-2021-15-6-33-39.

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The article deals with the problem of constructing a linear regression model based on incomplete data containing gaps, using statistical and expert information. The reasons for the gaps in the data can be, in particular, a temporary malfunction (failure) of the measuring equipment when taking various technical characteristics, or negligence in the work of statistical services when fixing the reporting indicators. Very often, gaps arise when processing various kinds of sociological information in the form of questionnaires, when respondents refuse to answer a specific question (but answer other

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24

Лютикова, Л. А. "A method for constructing a logical model for interpreting the decisions of a trained neural network." МОДЕЛИРОВАНИЕ, ОПТИМИЗАЦИЯ И ИНФОРМАЦИОННЫЕ ТЕХНОЛОГИИ 11, no. 4(43) (2023): 37–38. http://dx.doi.org/10.26102/2310-6018/2023.43.4.037.

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В данной работе предлагается метод интерпретации решений нейронных сетей, основанный на использовании булевого интегро-дифференциального исчисления. Этот метод позволяет исследовать логику принятия решений нейронными сетями и определить наиболее важные признаки, влияющие на их решения. Метод может быть применен для задач классификации, особенно в случаях, когда каждый признак может быть представлен как k-значная переменная. В работе рассматриваются локальная и глобальная интерпретации решений. На первом этапе происходит связывание каждого входного вектора с соответствующим выходом нейронной се

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25

Gao, Xiaoshan, and Zhenyu Huang. "Solving Boolean equation systems and applications in cryptanalysis." Science China Information Sciences 59, no. 5 (2016). http://dx.doi.org/10.1007/s11432-016-5548-2.

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26

Greve, Bjørn, Øyvind Ytrehus, Håvard Raddum, and Gunnar Fløystad. "Solving non-linear Boolean equation systems by variable elimination." Applicable Algebra in Engineering, Communication and Computing, August 17, 2019. http://dx.doi.org/10.1007/s00200-019-00399-7.

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27

A. Rushdi, A., and W. Ahmad. "Finding All Solutions of the Boolean Satisfiability Problem, If Any, via Boolean Equation Solving." مجلة جامعة الملك عبدالعزيز-العلوم الهندسية 27, no. 1 (2016). http://dx.doi.org/10.4197/eng.27-1.2.

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28

Manpreet, Singh, Singh Sandhu Parvinder, and Singh Kahlon Manjinder. "Faster FPGA Routing Solution using DNA Computing." December 24, 2007. https://doi.org/10.5281/zenodo.1086137.

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There are many classical algorithms for finding routing in FPGA. But Using DNA computing we can solve the routes efficiently and fast. The run time complexity of DNA algorithms is much less than other classical algorithms which are used for solving routing in FPGA. The research in DNA computing is in a primary level. High information density of DNA molecules and massive parallelism involved in the DNA reactions make DNA computing a powerful tool. It has been proved by many research accomplishments that any procedure that can be programmed in a silicon computer can be realized as a DNA computin

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29

Chen, Yu-Ao, and Xiao-Shan Gao. "Quantum Algorithm for Boolean Equation Solving and Quantum Algebraic Attack on Cryptosystems." Journal of Systems Science and Complexity, January 12, 2021. http://dx.doi.org/10.1007/s11424-020-0028-6.

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30

SMOLEV, V. V. "An approach to solving a Boolean linear equation with integer positive coefficients." Discrete Mathematics and Applications 3, no. 5 (1993). http://dx.doi.org/10.1515/dma.1993.3.5.523.

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31

Neele, Thomas, Tim A. C. Willemse, Wieger Wesselink, and Antti Valmari. "Partial-order reduction for parity games and parameterised Boolean equation systems." International Journal on Software Tools for Technology Transfer, October 2, 2022. http://dx.doi.org/10.1007/s10009-022-00672-0.

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AbstractIn model checking, reduction techniques can be helpful tools to fight the state-space explosion problem. Partial-order reduction (POR) is a well-known example, and many POR variants have been developed over the years. However, none of these can be used in the context of model checking stutter-sensitive temporal properties. We propose POR techniques for parity games, a well-established formalism for solving a variety of decision problems, including model checking. As a result, we obtain the first POR method that is sound for the full modal $$\upmu $$ μ -calculus. We show how our techniq

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32

Rushdi, Ali Muhammad Ali, and Fares Ahmad Muhammad Ghaleb. "Novel Characterizations of the JK Bistables (Flip Flops)." Journal of Engineering Research and Reports, April 3, 2019, 1–20. http://dx.doi.org/10.9734/jerr/2019/v4i316903.

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The JK flip flop is a flexible type of bistable elements that has extensive uses in digital electronics and control circuits. It is usually described by its characteristic equation or next-state table (used for analysis purposes) and its excitation table (used for synthesis purposes). This paper explores a variety of novel characterizations of JK flip flops. First, equational and implicational descriptions are presented, and methods of logic deduction are utilized to produce complete statements of all propositions that are true for a general JK flip flop. Next, methods of Boolean-equation solv

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33

I. Noskov, Sergey, and Egor S. Popov. "THE METHOD OF MIXED ESTIMATION OF REGRESSION MODEL PARAMETERS WITH AN ARBITRARY COMPOSITION OF OBSERVATION GROUPS." Models, systems, networks in economics, engineering, nature and society, no. 3 (2024). https://doi.org/10.21685/2227-8486-2024-3-8.

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Background. The construction of regression models of various complex objects in accordance with the objectives of the study is sometimes accompanied by the need to split the original data sample into subsamples (groups of observations) or the use of the so-called panel data. The purpose of the study is to modify the method for calculating estimates of the parameters of a linear regression equation developed earlier by one of the authors, using the mixed estimation method. Materials and methods. To achieve this goal, the mathematical apparatus for solving linear and linear Boolean programming p

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34

Edme, Quentin, Pierre-Alain Fouque, and André Schrottenloher. "Faster Quantum Algorithms for MQ2 and Applications." IACR Communications in Cryptology 2, no. 1 (2025). https://doi.org/10.62056/anjbksuc2.

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We study quantum algorithms for multivariate quadratic Boolean equation systems by focusing on their precise gate count. While better asymptotic algorithms are known, currently gate counts were only computed for exhaustive search (Schwabe and Westerbaan, SPACE 2016) and a variant of Grover's search using preprocessing (Pring, WAIFI 2018). This limits the applicability of Boolean equation solving to cryptanalysis, which considers relatively small numbers of variables (from 40 to 200) and is concerned with the exact complexity of the solver. In this paper, we introduce two new quantum algorithms

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35

Emmerson, Parker. "Conjunctions (I)." December 24, 2023. https://doi.org/10.5281/zenodo.10428738.

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This document explores the use of conjunctions in mathematical equations and how they can be used to represent complex systems. Conjunctions allow for a systematic approach to solving and analyzing equations, by breaking them down into smaller and more manageable parts. By using a mathematical induction, we can prove that equations involving conjunctions are true in all cases, making them applicable in various scenarios. This formulation allows for equations to be expressed abstractly, without a specific value for the parameters, which adds to their versatility. Overall, the use of conjunction

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36

Ustymenko, Vasyl. "On the cryptosystems based on two Eulerian transformations defined over the commutative rings Z2s, s>1." Theoretical and Applied Cybersecurity 6, no. 1 (2024). https://doi.org/10.20535/tacs.2664-29132024.1.317960.

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We suggest the family of ciphers sEn, n = 2, 3, ... with the space of plaintexts (Z2^s)^n, s > 1, such that the encryption map is the composition of kinds G = G1 A1 G2 A2, where Ai are the affine transformations from AGLn(Z2^s) preserving the variety (Z*2^s)^n. Eulerian endomorphisms Gi, i = 1, 2, of K[x1, x2, ..., xn] move xi to the monomial term M x1^d(1) x2^d(2) ... xn^d(n), M in Z2^s, and act on (Z2^s)^n as bijective transformations. The cipher is converted to a protocol-supported cryptosystem. Protocols of Noncommutative Cryptography implemented on the platform of Eulerian endomorphism

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