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Relevant bibliographies by topics / 'Big' Boolean algebras

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Academic literature on the topic ''Big' Boolean algebras'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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Journal articles on the topic "'Big' Boolean algebras"

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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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Terwijn, Sebastiaan A. "On the structure of the Medvedev lattice." Journal of Symbolic Logic 73, no. 2 (2008): 543–58. http://dx.doi.org/10.2178/jsl/1208359059.

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AbstractWe investigate the structure of the Medvedev lattice as a partial order. We prove that every interval in the lattice is either finite, in which case it is isomorphic to a finite Boolean algebra, or contains an antichain of size . the size of the lattice itself. We also prove that it is consistent with ZFC that the lattice has chains of size . and in fact that these big chains occur in every infinite interval. We also study embeddings of lattices and algebras. We show that large Boolean algebras can be embedded into the Medvedev lattice as upper semilattices, but that a Boolean algebra

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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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Тестов, В. А. "The role of mathematics in the formation of nonlinear thinking of schoolchildren and students." Математический вестник Вятского государственного университета, no. 1(20) (June 22, 2021): 28–32. http://dx.doi.org/10.25730/vsu.0536.21.005.

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В статье рассматривается трансдисциплинарная тенденция в содержании современного образования, выводящая синтез знаний на более высокий уровень, чем междисциплинарный. Благодаря этой тенденции появляются такие новые трансдисциплинарные области, как искусственный интеллект, большие данные и другие. Показывается, что в основе этой тенденции лежит процесс математизации знаний. Кроме того, в силу креативности методов, используемых при изучении математики, эта дисциплина становится основой формирования креативного потенциала личности. В статье рассматривается формирование у школьников и студентов не

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Rushdi, Ali, Sultan Zagzoog, and Ahmed Balamesh. "Design of a Hardware Circuit for Integer Factorization Using a Big Boolean Algebra." Journal of Advances in Mathematics and Computer Science 27, no. 1 (2018): 1–25. http://dx.doi.org/10.9734/jamcs/2018/40369.

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Pardo-Guerra, Sebastián, Hugo A. Rincón-Mejía, Manuel G. Zorrilla-Noriega, and Francisco González-Bayona. "On the lattice of conatural classes of linear modular lattices." Algebra universalis 84, no. 4 (2023). http://dx.doi.org/10.1007/s00012-023-00828-2.

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AbstractThe collection of all cohereditary classes of modules over a ring R is a pseudocomplemented complete big lattice. The elements of its skeleton are the conatural classes of R-modules. In this paper we extend some results about cohereditary classes in R-Mod to the category $$\mathcal {L_{M}}$$ L M of linear modular lattices, which has as objects all complete modular lattices and as morphisms all linear morphisms. We introduce the big lattice of conatural classes in $$\mathcal {L_{M}}$$ L M , and we obtain some results about it, paralleling the case of R-Mod and arriving at its being bool

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Dissertations / Theses on the topic "'Big' Boolean algebras"

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Chen, Xi, and 陈曦. "On construction and control of probabilistic Boolean networks." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2012. http://hub.hku.hk/bib/B48329605.

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Modeling gene regulation is an important problem in genomic research. The Boolean network (BN) and its generalization Probabilistic Boolean network (PBN) have been proposed to model genetic regulatory interactions. BN is a deterministic model while PBN is a stochastic model. In a PBN, on one hand, its stationary distribution gives important information about the long-run behavior of the network. On the other hand, one may be interested in system synthesis which requires the construction of networks from the observed stationary distribution. This results in an inverse problem of constructin

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Jiao, Yue, and 焦月. "Mathematical models for control of probabilistic Boolean networks." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2008. http://hub.hku.hk/bib/B41508634.

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Book chapters on the topic "'Big' Boolean algebras"

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Chang, Weng-Long, and Athanasios V. Vasilakos. "Boolean Algebra and Its Applications." In Studies in Big Data. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-63583-1_2.

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Conference papers on the topic "'Big' Boolean algebras"

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Tong, Yan, Huanguo Zhang, Zhengwei Ren, and Shiwei Xu. "Invariance of Algebraic Immunity of Vectorial Boolean Functions under Equivalence Relations." In 2020 IEEE 14th International Conference on Big Data Science and Engineering (BigDataSE). IEEE, 2020. http://dx.doi.org/10.1109/bigdatase50710.2020.00027.

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Liu, P., and J. N. Siddall. "Determination of the Minimum Evidence Set in Expert Systems Using Boolean Methods." In ASME 1989 Design Technical Conferences. American Society of Mechanical Engineers, 1989. http://dx.doi.org/10.1115/detc1989-0055.

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Abstract A new method is proposed for rapidly solving expert system applications using Boolean algebra formulations. The method consists of two algorithms, applied after the conventional hierarchical type rules have been converted to Boolean expressions. The first algorithm automatically reduces the expressions to the equivalent of only two levels in a logic network, eliminating all intermediate conclusions, and also minimizes the number of inputs per rule. This algorithm has general application in the condensation of rule systems, and makes possible the use of high speed bit matching in speci

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