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Relevant bibliographies by topics / Boolean-equation solving

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Academic literature on the topic 'Boolean-equation solving'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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Journal articles on the topic "Boolean-equation solving"

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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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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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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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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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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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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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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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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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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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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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Book chapters on the topic "Boolean-equation solving"

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Murphy, Sean, Maura Paterson, and Christine Swart. "Boolean Ring Cryptographic Equation Solving." In Selected Areas in Cryptography. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-81652-0_10.

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Keinänen, Misa, and Ilkka Niemelä. "Solving Alternating Boolean Equation Systems in Answer Set Programming." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/11415763_9.

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Groote, Jan Friso, and Misa Keinänen. "Solving Disjunctive/Conjunctive Boolean Equation Systems with Alternating Fixed Points." In Tools and Algorithms for the Construction and Analysis of Systems. Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-24730-2_33.

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Koolen, Ruud P. J., Tim A. C. Willemse, and Hans Zantema. "Using SMT for Solving Fragments of Parameterised Boolean Equation Systems." In Automated Technology for Verification and Analysis. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-24953-7_3.

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Neele, Thomas, Tim A. C. Willemse, and Jan Friso Groote. "Solving Parameterised Boolean Equation Systems with Infinite Data Through Quotienting." In Formal Aspects of Component Software. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-02146-7_11.

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Neele, Thomas, Tim A. C. Willemse, and Wieger Wesselink. "Partial-Order Reduction for Parity Games with an Application on Parameterised Boolean Equation Systems." In Tools and Algorithms for the Construction and Analysis of Systems. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-45237-7_19.

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Abstract Partial-order reduction (POR) is a well-established technique to combat the problem of state-space explosion. We propose POR techniques that are sound for parity games, a well-established formalism for solving a variety of decision problems. As a consequence, we obtain the first POR method that is sound for model checking for the full modal $$\mu $$-calculus. Our technique is applied to, and implemented for the fixed point logic called parameterised Boolean equation systems, which provides a high-level representation of parity games. Experiments indicate that substantial reductions ca

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Stramaglia, Anna, Jeroen J. A. Keiren, Maurice Laveaux, and Tim A. C. Willemse. "Efficient Evidence Generation for Modal $$\mu $$-Calculus Model Checking." In Lecture Notes in Computer Science. Springer Nature Switzerland, 2025. https://doi.org/10.1007/978-3-031-90643-5_10.

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Abstract Model checking is a technique to automatically establish whether a model of the behaviour of a system meets its requirements. Evidence explaining why the behaviour does (not) meet its requirements is essential for the user to understand the model checking result. Willemse and Wesselink showed that parameterised Boolean equation systems (PBESs), an intermediate format for $$\mu $$ μ -calculus model checking, can be extended with information to generate such evidence. Solving the resulting PBES is much slower than solving one without additional information, and sometimes even impossible

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Conference papers on the topic "Boolean-equation solving"

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Lin, Wan-Hsuan, Chia-Hsuan Su, and Jie-Hong R. Jiang. "Language Equation Solving via Boolean Automata Manipulation." In ICCAD '22: IEEE/ACM International Conference on Computer-Aided Design. ACM, 2022. http://dx.doi.org/10.1145/3508352.3549428.

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