Relevant bibliographies by topics / Boolean equation

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Boolean equation'

Author: Grafiati
Published: 5 June 2025
Last updated: 1 August 2025

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Journal articles on the topic "Boolean equation"

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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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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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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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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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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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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'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'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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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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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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Dissertations / Theses on the topic "Boolean equation"

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Feliú, Gabaldón Marco Antonio. "Logic-based techniques for program analysis and specification synthesis." Doctoral thesis, Universitat Politècnica de València, 2013. http://hdl.handle.net/10251/33747.

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La Tesis investiga técnicas ágiles dentro del paradigma declarativo para dar solución a dos problemas: el análisis de programas y la inferencia de especificaciones a partir de programas escritos en lenguajes multiparadigma y en lenguajes imperativos con tipos, objetos, estructuras y punteros. Respecto al estado actual de la tesis, la parte de análisis de programas ya está consolidada, mientras que la parte de inferencia de especificaciones sigue en fase de desarrollo activo. La primera parte da soluciones para la ejecución de análisis de punteros especificados en Datalog. En esta parte se han
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Zhu, Guangwen. "Structural Stability Conditions for Boolean Delay Equations." Ohio University / OhioLINK, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1213731021.

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Yeum, Ji-A. "Probability of Solvability of Random Systems of 2-Linear Equations over GF(2)." Columbus, Ohio : Ohio State University, 2008. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1230149164.

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Schwieger, Robert [Verfasser]. "Combining Boolean Networks and Ordinary Differential Equations for Analysis and Comparison of Gene Regulatory Networks / Robert Schwieger." Berlin : Freie Universität Berlin, 2019. http://d-nb.info/1191755916/34.

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Sinak, Ahmet. "On Verification Of Restricted Extended Affine Equivalence Of Vectorial Boolean Functions." Master's thesis, METU, 2012. http://etd.lib.metu.edu.tr/upload/12615191/index.pdf.

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Vectorial Boolean functions are used as S-boxes in cryptosystems. To design inequivalent vectorial Boolean functions resistant to known attacks is one of the challenges in cryptography. Verifying whether two vectorial Boolean functions are equivalent or not is the final step in this challenge. Hence, finding a fast technique for determining whether two given vectorial Boolean functions are equivalent is an important problem. A special class of the equivalence called restricted extended affine (REA) equivalence is studied in this thesis. We study the verification complexity of REA-equivalence
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Gindullin, Ramiz. "Learning concise constraint models from error-free data : studies on learning Boolean-arithmetic equations and short-term scheduling models." Electronic Thesis or Diss., Ecole nationale supérieure Mines-Télécom Atlantique Bretagne Pays de la Loire, 2024. http://www.theses.fr/2024IMTA0393.

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Utilisant la programmation logique par contrainte, l'objectif de cette thèse est de développer plusieurs techniques d'acquisition de contraintes pour les situations où nous disposons de données sans erreur. De telles situations rendent la majorité des techniques de ML inutilisables et de nouvelles approches sont nécessaires. Les techniques d'acquisition de contraintes proposées sont appliquées à deux cas d'utilisation : la recherche de nouvelles conjectures de limites fortes pour huit objets combinatoires et l'acquisition de contraintes à partir d'un calendrier de production à court terme uniq
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Bhupatiraju, Raja D. V. "A comparative study of high speed adders." Ohio : Ohio University, 1999. http://www.ohiolink.edu/etd/view.cgi?ohiou1175891877.

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Vaginay, Athénaïs. "Synthesis of Boolean Networks from the Structure and Dynamics of Reaction Networks." Electronic Thesis or Diss., Université de Lorraine, 2023. http://www.theses.fr/2023LORR0135.

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La conversion entre différent formalismes de modélisation est un défi majeur en biologie des systèmes, car elle aide à obtenir de nouvelles connaissances sur les systèmes biologiques. Cette thèse propose une approche pour synthétiser automatiquement des réseaux Booléens à partir de réseaux de réactions existants, permettant la conversion entre deux formalismes très utilisés. La thèse se compose de trois contributions. La première concerne l'extraction de la structure et de la dynamique d'un réseau de réactions : un graphe qui encode les potentielles influences directes entre les composants du
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Minucci, Sarah B. "Mathematical Models of the Inflammatory Response in the Lungs." VCU Scholars Compass, 2017. https://scholarscompass.vcu.edu/etd/5191.

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Inflammation in the lungs can occur for many reasons, from bacterial infections to stretch by mechanical ventilation. In this work we compare and contrast various mathematical models for lung injuries in the categories of acute infection, latent versus active infection, and particulate inhalation. We focus on systems of ordinary differential equations (ODEs), agent-based models (ABMs), and Boolean networks. Each type of model provides different insight into the immune response to damage in the lungs. This knowledge includes a better understanding of the complex dynamics of immune cells, protei
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Ben, Ghorbal Anis. "Fondements algébriques des probabilités quantiques et calcul stochastique sur l'espace de Fock booléen." Nancy 1, 2001. http://www.theses.fr/2001NAN10009.

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Ce mémoire est divisé en trois grandes parties. La première est consacrée essentiellement à l'étude des produits en probabilités quantiques. Nous donnons une classification complète à l'aide du produit universel défini par un ensemble d'axiomes canoniques dans les différentes catégories d'algèbres associatives. Ceci nous permet aussi de définir la notion d'indépendance stochastique non-commutative. En particulier nous démontrons que les seuls produits sont les produits tensoriel (classique), libre et booléen. La seconde partie est motivée directement par la première. Elle est consacrée à l'étu
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Books on the topic "Boolean equation"

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Steinbach, Bernd, and Christian Posthoff. Boolean Differential Equations. Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-031-79861-0.

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Brown, Frank Markham. Boolean Reasoning: The Logic of Boolean Equations. Springer US, 1990.

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Brown, Frank Markham. Boolean reasoning: The logic of Boolean equations. Kluwer Academic Publishers, 1990.

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Brown, Frank Markham. Boolean reasoning: The logic of Boolean equations. 2nd ed. Dover Publications, 2003.

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Steinbach, Posthoff. Boolean Differential Equations. Morgan & Claypool Publishers, 2013.

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Posthoff, Christian, and Bernd Steinbach. Boolean Differential Equations. Springer International Publishing AG, 2013.

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Posthoff, Christian, and Bernd Steinbach. Boolean Differential Equations. Morgan & Claypool Publishers, 2013.

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Brown, Frank Markham. Boolean Reasoning: The Logic of Boolean Equations. Dover Publications, Incorporated, 2012.

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Posthoff, Christian, and Bernd Steinbach. Boolean Differential Equations: Responses to China's Belt and Road Initiative. Springer International Publishing AG, 2022.

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Book chapters on the topic "Boolean equation"

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Li, Haitao, Xinrong Yang, and Wenrong Li. "Boolean Determinant and Boolean Equation." In From Boolean Matrix Theory to Logical Dynamical Systems. Springer Nature Singapore, 2025. https://doi.org/10.1007/978-981-96-2967-1_3.

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Groote, Jan Friso, and Tim Willemse. "Parameterised Boolean Equation Systems." In CONCUR 2004 - Concurrency Theory. Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-28644-8_20.

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Chiossi, Simon G. "Boolean Algebras "Equation missing"." In Essential Mathematics for Undergraduates. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-87174-1_5.

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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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Orzan, Simona, and Tim A. C. Willemse. "Invariants for Parameterised Boolean Equation Systems." In CONCUR 2008 - Concurrency Theory. Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-85361-9_18.

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van Dam, A., B. Ploeger, and T. A. C. Willemse. "Instantiation for Parameterised Boolean Equation Systems." In Theoretical Aspects of Computing - ICTAC 2008. Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-85762-4_30.

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Gazda, Maciej W., and Tim A. C. Willemse. "Consistent Consequence for Boolean Equation Systems." In SOFSEM 2012: Theory and Practice of Computer Science. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-27660-6_23.

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Keiren, Jeroen J. A., and Tim A. C. Willemse. "Bisimulation Minimisations for Boolean Equation Systems." In Hardware and Software: Verification and Testing. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-19237-1_12.

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Cranen, Sjoerd, Bas Luttik, and Tim A. C. Willemse. "Proof Graphs for Parameterised Boolean Equation Systems." In CONCUR 2013 – Concurrency Theory. Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-40184-8_33.

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Keiren, Jeroen J. A., Wieger Wesselink, and Tim A. C. Willemse. "Liveness Analysis for Parameterised Boolean Equation Systems." In Automated Technology for Verification and Analysis. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-11936-6_16.

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Conference papers on the topic "Boolean equation"

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Huang, Jinglian, and Xiujuan Yuan. "The e-derivative Boolean differential equation and logic circuit detection." In 2025 6th International Conference on Computing, Networks and Internet of Things (CNIOT). IEEE, 2025. https://doi.org/10.1109/cniot65435.2025.11071012.

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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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Gallardo, María del Mar, Christophe Joubert, and Pedro Merino. "Implementing Influence Analysis Using Parameterised Boolean Equation Systems." In Second International Symposium on Leveraging Applications of Formal Methods, Verification and Validation (isola 2006). IEEE, 2006. http://dx.doi.org/10.1109/isola.2006.26.

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Mateescu, Radu, and Emilie Oudot. "Bisimulator 2.0: An On-the-Fly Equivalence Checker based on Boolean Equation Systems." In 2008 6th ACM/IEEE International Conference on Formal Methods and Models for Codesign (MEMOCODE '08). IEEE, 2008. http://dx.doi.org/10.1109/memcod.2008.4547690.

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Can, Yavuz, and Georg Fischer. "New orthogonalizing Boolean equation using in the calculation of test patterns for combinatorial circuits." In 2015 9th International Conference on Electrical and Electronics Engineering (ELECO). IEEE, 2015. http://dx.doi.org/10.1109/eleco.2015.7394481.

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Kumar, Ashok V., Jongho Lee, and Ravi Burla. "Implicit Solid Modeling for Mesh Free Analysis." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-85402.

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In traditional solid modeling the boundaries of the solid are represented using parametric equations. Even though the application of implicit equations has also been explored, they have not been widely used. Interest has been rekindled recently due to application of implicit equations to mesh free engineering analysis. In this paper, an implicit representation scheme for solids is presented where the boundaries of primitive solids are defined using implicit equation of surfaces. To ensure that the equations are axis independent, the characteristic functions for the implicit equations are defin
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Bachrathy, Daniel, and Gabor Stepan. "Fold Bifurcation in the State-Dependent Delay Model of Milling: Analytical and Numerical Solutions." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-48300.

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The standard models of the milling process describe the surface regeneration effect by a delay-differential equation with constant time delay. In this study, an improved two degree of freedom model is presented for milling process where the regenerative effect is described by an improved state dependent time delay model. The model contains exact nonlinear screen functions describing the entrance and exit positions of the cutting edges of the milling tool. This model is valid in case of large amplitude forced vibrations close to the near-resonant spindle speeds. The periodic motions of this non
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Peng, Xiaobo, Weihan Zhang, Sai-Gowthami Asam, and Ming C. Leu. "Surface Reconstruction From Dexel Data for Virtual Sculpting." In ASME 2004 International Mechanical Engineering Congress and Exposition. ASMEDC, 2004. http://dx.doi.org/10.1115/imece2004-61580.

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This paper presents a new method for surface reconstruction from dexel data for virtual sculpting. We are in the midst of developing a dexel model based sculpting system having the capability of interactive solid modeling with haptics interface. The geometric modeling of our sculpting system is based on the Sweep Differential Equation method to compute the boundary of the tool swept volume. Ray casting is used to perform Boolean operations between the tool swept volume and the virtual stock in dexel models to simulate the sculpting process. The dexel data are converted to a series of planar co
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Qi, Hongsheng, Bo Li, Rui-Juan Jing, Alexandre Proutiere, and Guodong Shi. "Distributedly Solving Boolean Equations over Networks." In 2020 59th IEEE Conference on Decision and Control (CDC). IEEE, 2020. http://dx.doi.org/10.1109/cdc42340.2020.9304144.

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Stankovic, Ivan, Jelena Ignjatovic, and Miroslav Ciric. "Boolean relation equations in data analysis." In 2011 IEEE 9th International Symposium on Intelligent Systems and Informatics (SISY 2011). IEEE, 2011. http://dx.doi.org/10.1109/sisy.2011.6034306.

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Reports on the topic "Boolean equation"

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Baader, Franz, and Alexander Okhotin. On Language Equations with One-sided Concatenation. Aachen University of Technology, 2006. http://dx.doi.org/10.25368/2022.154.

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Language equations are equations where both the constants occurring in the equations and the solutions are formal languages. They have first been introduced in formal language theory, but are now also considered in other areas of computer science. In the present paper, we restrict the attention to language equations with one-sided concatenation, but in contrast to previous work on these equations, we allow not just union but all Boolean operations to be used when formulating them. In addition, we are not just interested in deciding solvability of such equations, but also in deciding other prop
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Baader, Franz, and Alexander Okhotin. Solving Language Equations and Disequations Using Looping Tree Automata with Colors. Technische Universität Dresden, 2012. http://dx.doi.org/10.25368/2022.185.

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We extend previous results on the complexity of solving language equations with one-sided concatenation and all Boolean operations to the case where also disequations (i.e., negated equations) may occur. To show that solvability of systems of equations and disequations is still in ExpTime, we introduce a new type of automata working on infinite trees, which we call looping automata with colors. As applications of these results, we show new complexity results for disunification in the description logic FL₀ and for monadic set constraints with negation. We believe that looping automata with colo
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Baader, Franz, Silvio Ghilardi, and Cesare Tinelli. A New Combination Procedure for the Word Problem that Generalizes Fusion Decidability Results in Modal Logics. Technische Universität Dresden, 2003. http://dx.doi.org/10.25368/2022.130.

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Previous results for combining decision procedures for the word problem in the non-disjoint case do not apply to equational theories induced by modal logics - which are not disjoint for sharing the theory of Boolean algebras. Conversely, decidability results for the fusion of modal logics are strongly tailored towards the special theories at hand, and thus do not generalize to other types of equational theories. In this paper, we present a new approach for combining decision procedures for the word problem in the non-disjoint case that applies to equational theories induced by modal logics, bu
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