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Relevant bibliographies by topics / Algebra, Boolean

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Academic literature on the topic 'Algebra, Boolean'

Author: Grafiati

Published: 4 June 2021

Last updated: 29 July 2024

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Journal articles on the topic "Algebra, Boolean"

1

Bezhanishvili, Guram, and Patrick J. Morandi. "Profinite Heyting Algebras and Profinite Completions of Heyting Algebras." gmj 16, no. 1 (2009): 29–47. http://dx.doi.org/10.1515/gmj.2009.29.

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Abstract This paper surveys recent developments in the theory of profinite Heyting algebras (resp. bounded distributive lattices, Boolean algebras) and profinite completions of Heyting algebras (resp. bounded distributive lattices, Boolean algebras). The new contributions include a necessary and sufficient condition for a profinite Heyting algebra (resp. bounded distributive lattice) to be isomorphic to the profinite completion of a Heyting algebra (resp. bounded distributive lattice). This results in simple examples of profinite bounded distributive lattices that are not isomorphic to the pro

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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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Ehrenfeucht, Andrzej, and Marek W. Zawadowski. "A Representation of Partial Boolean Algebras." Fundamenta Informaticae 16, no. 3-4 (1992): 349–53. http://dx.doi.org/10.3233/fi-1992-163-408.

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Knight, Julia F., and Michael Stob. "Computable Boolean algebras." Journal of Symbolic Logic 65, no. 4 (2000): 1605–23. http://dx.doi.org/10.2307/2695066.

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Feiner [F] showed that a Boolean algebra need not have a computable copy (see also [T2]). Downey and Jockusch [D-J] showed that every low Boolean algebra does have a computable copy. Thurber [T3], showed that every low2 Boolean algebra has a computable copy. Here we show that every Boolean algebra which is low3, or even low4, has a computable copy.The results of [D-J] and [T3] were obtained by passing to linear orderings. In [D-J], there is an embedding theorem saying that any linear ordering which is with the successor relation as an added predicate can be embedded in a slightly larger linear

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BEZHANISHVILI, NICK, and WESLEY H. HOLLIDAY. "CHOICE-FREE STONE DUALITY." Journal of Symbolic Logic 85, no. 1 (2019): 109–48. http://dx.doi.org/10.1017/jsl.2019.11.

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AbstractThe standard topological representation of a Boolean algebra via the clopen sets of a Stone space requires a nonconstructive choice principle, equivalent to the Boolean Prime Ideal Theorem. In this article, we describe a choice-free topological representation of Boolean algebras. This representation uses a subclass of the spectral spaces that Stone used in his representation of distributive lattices via compact open sets. It also takes advantage of Tarski’s observation that the regular open sets of any topological space form a Boolean algebra. We prove without choice principles that an

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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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Bonnet, Robert, and Matatyahu Rubin. "Elementary embedding between countable Boolean algebras." Journal of Symbolic Logic 56, no. 4 (1991): 1212–29. http://dx.doi.org/10.2307/2275469.

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AbstractFor a complete theory of Boolean algebras T, let MT denote the class of countable models of T. For B1, B2 ∈ MT, let B1 ≤ B2 mean that B2 is elementarily embeddable in B2. Theorem 1. For every complete theory of Boolean algebras T, if T ≠ Tω, then ‹MT, ≤› is well-quasi-ordered. ∎ We define Tω. For a Boolean algebra B, let I(B) be the ideal of all elements of the form a + s such that B ↾ a is an atomic Boolean algebra and B ↾ s is an atomless Boolean algebra. The Tarski derivative of B is defined as follows: B(0) = B and B(n + 1) = B(n)/I(B(n)). Define Tω to be the theory of all Boolean

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Paad, Akbar. "Ideals in bounded equality algebras." Filomat 33, no. 7 (2019): 2113–23. http://dx.doi.org/10.2298/fil1907113p.

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In this paper, the concept of ideal in bounded equality algebras is introduced. With respect to this concepts, some related results are given. In particular, we prove that there is an one-to-one corresponding between congruence relation on an involutive equality algebra and the set of ideals on it. Also, we prove the first isomorphism theorem on equality algebras. Moreover, the notions of prime and Boolean ideals in equality algebras are introduced. Finally, we prove that ideal I of involutive prelinear equality algebra E is a Boolean ideal if and only if E/I is a Boolean algebra.

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Rao, G. C., and P. Sundarayya. "Boolean Algebra of C-Algebras." ITB Journal of Sciences 44, no. 3 (2012): 204–16. http://dx.doi.org/10.5614/itbj.sci.2012.44.3.1.

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Džamonja, Mirna, and Grzegorz Plebanek. "Strictly positive measures on Boolean algebras." Journal of Symbolic Logic 73, no. 4 (2008): 1416–32. http://dx.doi.org/10.2178/jsl/1230396929.

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AbstractWe investigate strictly positive finitely additive measures on Boolean algebras and strictly positive Radon measures on compact zerodimensional spaces. The motivation is to find a combinatorial characterisation of Boolean algebras which carry a strictly positive finitely additive finite measure with some additional properties, such as separability or nonatomicity. A possible consistent characterisation for an algebra to carry a separable strictly positive measure was suggested by Talagrand in 1980, which is that the Stone space K of the algebra satisfies that its space M(K) of measures

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Dissertations / Theses on the topic "Algebra, Boolean"

1

Schardijn, Amy. "AN INTRODUCTION TO BOOLEAN ALGEBRAS." CSUSB ScholarWorks, 2016. https://scholarworks.lib.csusb.edu/etd/421.

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This thesis discusses the topic of Boolean algebras. In order to build intuitive understanding of the topic, research began with the investigation of Boolean algebras in the area of Abstract Algebra. The content of this initial research used a particular notation. The ideas of partially ordered sets, lattices, least upper bounds, and greatest lower bounds were used to define the structure of a Boolean algebra. From this fundamental understanding, we were able to study atoms, Boolean algebra isomorphisms, and Stone’s Representation Theorem for finite Boolean algebras. We also verified and prove

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Bell, Steven. "Modular homology in the Boolean algebra." Thesis, University of East Anglia, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.368141.

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Tarnoff, David. "Episode 4.05 – Introduction to Boolean Algebra." Digital Commons @ East Tennessee State University, 2020. https://dc.etsu.edu/computer-organization-design-oer/33.

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Truth tables and circuit diagrams fall short in many ways including their abilities to evaluate and manipulate combinational logic. By using algebraic methods to represent logic expressions, we can apply properties and identities to improve performance.

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Tarnoff, David. "Episode 4.06 – Properties of Boolean Algebra." Digital Commons @ East Tennessee State University, 2020. https://dc.etsu.edu/computer-organization-design-oer/34.

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Tarnoff, David. "Episode 4.07 – Identities of Boolean Algebra." Digital Commons @ East Tennessee State University, 2020. https://dc.etsu.edu/computer-organization-design-oer/35.

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We are familiar with algebraic laws such as multiply zero by anything, and we get zero. In this episode, we see how a Boolean expression containing a constant, a duplicated signal, or a signal being combined with its inverse will simplify…always.

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Van, Name Joseph Anthony. "Boolean Partition Algebras." Scholar Commons, 2013. http://scholarcommons.usf.edu/etd/4599.

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A Boolean partition algebra is a pair $(B,F)$ where $B$ is a Boolean algebra and $F$ is a filter on the semilattice of partitions of $B$ where $\bigcup F=B\setminus\{0\}$. In this dissertation, we shall investigate the algebraic theory of Boolean partition algebras and their connection with uniform spaces. In particular, we shall show that the category of complete non-Archimedean uniform spaces is equivalent to a subcategory of the category of Boolean partition algebras, and notions such as supercompleteness of non-Archimedean uniform spaces can be formulated in terms of Boolean partition alg

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Schimanski, Nichole Louise. "Orthomorphisms of Boolean Groups." PDXScholar, 2016. http://pdxscholar.library.pdx.edu/open_access_etds/3100.

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An orthomorphism, π, of a group, (G, +), is a permutation of G with the property that the map x → -x + π(x) is also a permutation. In this paper, we consider orthomorphisms of the additive group of binary n-tuples, Zn2. We use known orthomorphism preserving functions to prove a uniformity in the cycle types of orthomorphisms that extend certain partial orthomorphisms, and prove that extensions of particular sizes of partial orthomorphisms exist. Further, in studying the action of conjugating orthomorphisms by automorphisms, we find several symmetries within the orbits and stabilizers of this a

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Geschke, Stefan. "On s-filtered [sigma-filtered] Boolean algebras." [S.l. : s.n.], 1999. http://www.diss.fu-berlin.de/2000/70/index.html.

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Hadida, Ahmed Mohamed. "A partially ordered semigroup of Boolean spaces." Diss., The University of Arizona, 1988. http://hdl.handle.net/10150/184369.

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In this thesis we are concerned with arithmetic in a certain partially ordered, commutative semigroup D. The first chapter investigates the class of countable Boolean algebras from which this semigroup arises. The elements of D correspond to the isomorphism classes of the Boolean algebras under consideration. In Chapter 2 we begin the study of the semigroup structure of D. D is axiomatically described by three groups of axioms. It is proved that these axioms are categorical. The ordering of D is used to investigate the multiplication. The set of T of torsion elements of D (elements with only f

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Bozeman, Alan Kyle. "Weakly Dense Subsets of Homogeneous Complete Boolean Algebras." Thesis, University of North Texas, 1990. https://digital.library.unt.edu/ark:/67531/metadc330803/.

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The primary result from this dissertation is following inequality: d(B) ≤ min(2^< wd(B),sup{λ^c(B): λ < wd(B)}) in ZFC, where B is a homogeneous complete Boolean algebra, d(B) is the density, wd(B) is the weak density, and c(B) is the cellularity of B. Chapter II of this dissertation is a general overview of homogeneous complete Boolean algebras. Assuming the existence of a weakly inaccessible cardinal, we give an example of a homogeneous complete Boolean algebra which does not attain its cellularity. In chapter III, we prove that for any integer n > 1, wd_2(B) = wd_n(B). Also in this chapt

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Books on the topic "Algebra, Boolean"

1

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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Kusraev, A. G. Boolean valued analysis. Kluwer Academic, 1999.

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(1990), LMS Durham Symposium. Boolean function complexity. Cambridge University Press, 1992.

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A, Riber K., Halmos Paul, Axler Sheldon Jay, and SpringerLink (Online service), eds. Introduction to Boolean Algebras. Springer New York, 2009.

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Whitesitt, J. Eldon. Boolean algebra and its applications. Dover Publications, 1995.

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Abad, Manuel. Monadic symmetric Boolean algebras. INMABB, 1989.

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Pinus, A. G. Constructions of Boolean algebras. Novosibirsk State Technical University, 1994.

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Hailperin, Theodore. Boole's logic and probability: A critical exposition from the standpoint of contemporary algebra, logic, and probability theory. 2nd ed. North-Holland Pub. Co., 1986.

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Pinus, A. G. Boolean constructions in universal algebras. Kluwer Academic, 1993.

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Book chapters on the topic "Algebra, Boolean"

1

Hailperin, Theodore. "Boole’s Algebra Isn’t Boolean Algebra." In A Boole Anthology. Springer Netherlands, 2000. http://dx.doi.org/10.1007/978-94-015-9385-4_4.

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Hardy, Yorick, and Willi-Hans Steeb. "Boolean Algebra." In Classical and Quantum Computing. Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8366-5_2.

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Hsu, John Y. "Boolean Algebra." In Computer Logic. Springer New York, 2002. http://dx.doi.org/10.1007/978-1-4613-0047-2_2.

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Borowik, Bohdan, Mykola Karpinskyy, Valery Lahno, and Oleksandr Petrov. "Boolean Algebra." In Intelligent Systems, Control and Automation: Science and Engineering. Springer Netherlands, 2012. http://dx.doi.org/10.1007/978-94-007-5228-3_5.

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Gårding, Lars, and Torbjörn Tambour. "Boolean algebra." In Algebra for Computer Science. Springer US, 1988. http://dx.doi.org/10.1007/978-1-4613-8797-8_10.

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Seiffertt, John. "Boolean Algebra." In Digital Logic for Computing. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-56839-3_2.

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Krantz, Steven G. "Boolean Algebra." In Handbook of Logic and Proof Techniques for Computer Science. Birkhäuser Boston, 2002. http://dx.doi.org/10.1007/978-1-4612-0115-1_13.

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Weik, Martin H. "Boolean algebra." In Computer Science and Communications Dictionary. Springer US, 2000. http://dx.doi.org/10.1007/1-4020-0613-6_1765.

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Ganney, Paul S. "Boolean Algebra." In Introduction to Bioinformatics and Clinical Scientific Computing. CRC Press, 2022. http://dx.doi.org/10.1201/9781003316244-6.

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Andonov, Sasho. "Boolean Algebra." In Bowtie Methodology. CRC Press, 2017. http://dx.doi.org/10.1201/9781315158853-4.

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Conference papers on the topic "Algebra, Boolean"

1

Swamy, U. M. "Sheaves Over Boolean Spaces." In The International Conference on Algebra 2010 - Advances in Algebraic Structures. WORLD SCIENTIFIC, 2011. http://dx.doi.org/10.1142/9789814366311_0049.

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Azram, M., J. I. Daoud, and F. A. M. Elfaki. "Arithmetic version of Boolean algebra." In 2009 2nd IEEE International Conference on Computer Science and Information Technology. IEEE, 2009. http://dx.doi.org/10.1109/iccsit.2009.5234473.

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Chattopadhyay, Anupam, Luca Amaru, Mathias Soeken, Pierre-Emmanuel Gaillardon, and Giovanni De Micheli. "Notes on Majority Boolean Algebra." In 2016 IEEE 46th International Symposium on Multiple-Valued Logic (ISMVL). IEEE, 2016. http://dx.doi.org/10.1109/ismvl.2016.21.

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Bosco, Alessio, Luca Biader-Ceipidor, Eugenio Fazio, and Mario Bertolotti. "All-optical parallel Boolean algebra." In Photonics Europe, edited by Hugo Thienpont, Kent D. Choquette, and Mohammad R. Taghizadeh. SPIE, 2004. http://dx.doi.org/10.1117/12.545873.

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Radojevic, Dragan. "Interpolative realization of Boolean algebra." In 2006 8th Seminar on Neural Network Applications in Electrical Engineering. IEEE, 2006. http://dx.doi.org/10.1109/neurel.2006.341214.

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Đorđević, Suzana. "PRIMENA INFORMACIONIH TEHNOLOGIJA U NASTAVI BULOVE ALGEBRE." In Metodički aspekti nastave matematike. Faculty of Edaucatin in Jagodina, 2021. http://dx.doi.org/10.46793/manm4.112dj.

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In various scientific disciplines, especially in mathematics, com- puter science, technology, economy, sociology and medicine, solutions to many problems can be transformed in the form of “yes” or “no” or “0” or “1”. This fact, among other things, accelerated the development of electronics and digital tech- nology, and thus Boolean algebra, especially two-valued Boolean algebra. The pa- per contains three chapters. The first chapter discusses the definition of Boolean algebra, two-valued Boolean algebra and Boolean functions. The second chapter deals with the application of Boolean algebra in

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Anitha, V., and B. Poorna. "DNA Sequence Matching Using Boolean Algebra." In 2010 International Conference on Advances in Computer Engineering (ACE). IEEE, 2010. http://dx.doi.org/10.1109/ace.2010.87.

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Beckhoff, Gerhard. "Discrete interference modeling via boolean algebra." In 2011 33rd Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE, 2011. http://dx.doi.org/10.1109/iembs.2011.6089921.

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Xu, Youjun, Dantong Ouyang, Yuxin Ye, and Jialiang He. "Solving SAT Problem with Boolean Algebra." In 2010 Fifth International Conference on Frontier of Computer Science and Technology (FCST). IEEE, 2010. http://dx.doi.org/10.1109/fcst.2010.13.

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Honglan Liu, Qingshi Gao, and Weidong Hao. "Probabilistic logic system is Boolean algebra homomorphic with set algebra." In 2010 International Conference on Progress in Informatics and Computing (PIC). IEEE, 2010. http://dx.doi.org/10.1109/pic.2010.5687410.

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Reports on the topic "Algebra, Boolean"

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McCune, W. Single axioms for Boolean algebra. Office of Scientific and Technical Information (OSTI), 2000. http://dx.doi.org/10.2172/764208.

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Veroff, R., and W. McCune. A Short Sheffer axiom for Boolean algebra. Office of Scientific and Technical Information (OSTI), 2000. http://dx.doi.org/10.2172/764209.

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Barnett, Janet Heine. Applications of Boolean Algebra: Claude Shannon and Circuit Design. The MAA Mathematical Sciences Digital Library, 2013. http://dx.doi.org/10.4169/loci004000.

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Barnett, Janet Heine. Boolean Algebra as an Abstract Structure: Edward V. Huntington and Axiomatization. The MAA Mathematical Sciences Digital Library, 2013. http://dx.doi.org/10.4169/loci003998.

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Barnett, Janet Heine. Origins of Boolean Algebra in the Logic of Classes: George Boole, John Venn and C. S. Peirce. The MAA Mathematical Sciences Digital Library, 2013. http://dx.doi.org/10.4169/loci003997.

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Baader, Franz. Concept Descriptions with Set Constraints and Cardinality Constraints. Technische Universität Dresden, 2017. http://dx.doi.org/10.25368/2022.232.

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We introduce a new description logic that extends the well-known logic ALCQ by allowing the statement of constraints on role successors that are more general than the qualified number restrictions of ALCQ. To formulate these constraints, we use the quantifier-free fragment of Boolean Algebra with Presburger Arithmetic (QFBAPA), in which one can express Boolean combinations of set constraints and numerical constraints on the cardinalities of sets. Though our new logic is considerably more expressive than ALCQ, we are able to show that the complexity of reasoning in it is the same as in ALCQ, bo

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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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