Relevant bibliographies by topics / Algebra, Boolean

Contents

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

Academic literature on the topic 'Algebra, Boolean'

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Published: 4 June 2021
Last updated: 29 July 2024

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Journal articles on the topic "Algebra, Boolean"

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Bezhanishvili, Guram, and Patrick J. Morandi. "Profinite Heyting Algebras and Profinite Completions of Heyting Algebras." gmj 16, no. 1 (March 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 profinite completion of any bounded distributive lattice. We also show that each profinite Boolean algebra is isomorphic to the profinite completion of some Boolean algebra. It is still an open question whether each profinite Heyting algebra is isomorphic to the profinite completion of some Heyting algebra.
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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 (January 2, 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 by using a conventional method and a novel one for deriving parametric general solutions, and subsequently utilizing expansion trees for generating all particular solutions of the aforementioned Boolean equation. Each of these two methods could be cast in pure algebraic form, but becomes much easier to visualize and comprehend when presented via the natural map of a big Boolean algebra, which (for historical reasons) is called the variable-entered Karnaugh map (VEKM). In the classical method, the number of parameters used is minimized and compact solutions are obtained. However, the parameters belong to the underlying big Boolean algebra. By contrast, the novel method does not attempt to minimize the number of parameters used, as it uses independent parameters belonging to the two-valued Boolean algebra B2 for each asserted atom in the Boole-Shannon expansion of the formula ݃(ࢄ .(Though the method produces non-compact expressions, it is much quicker in generating particular solutions. The two methods are demonstrated via two detailed examples.
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Ehrenfeucht, Andrzej, and Marek W. Zawadowski. "A Representation of Partial Boolean Algebras." Fundamenta Informaticae 16, no. 3-4 (May 1, 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 (December 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 ordering which is computable. An isomorphism theorem of Remmel [R] is used to show that the interval algebras of the two linear orderings are isomorphic (except in a trivial case). In [T3], there is an embedding theorem saying that any linear ordering which is with certain added predicates can be embedded in one which is with successor. Again the isomorphism theorem of Remmel is used to show that the interval algebras are isomorphic (except in a trivial case).Here, instead of passing to linear orderings, we work directly with Boolean algebras. We begin with a review of the known results. We re-formulate the embedding theorems of Downey-Jockusch and Thurber in terms of Boolean algebras. We extract from Remmel's isomorphism theorem some information on complexity. In this way, we show that a low Boolean algebra is isomorphic to a computable one by an isomorphism which is , at worst, and the same is true for a low2 Boolean algebra.
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BEZHANISHVILI, NICK, and WESLEY H. HOLLIDAY. "CHOICE-FREE STONE DUALITY." Journal of Symbolic Logic 85, no. 1 (August 29, 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 any Boolean algebra arises from a special spectral space X via the compact regular open sets of X; these sets may also be described as those that are both compact open in X and regular open in the upset topology of the specialization order of X, allowing one to apply to an arbitrary Boolean algebra simple reasoning about regular opens of a separative poset. Our representation is therefore a mix of Stone and Tarski, with the two connected by Vietoris: the relevant spectral spaces also arise as the hyperspace of nonempty closed sets of a Stone space endowed with the upper Vietoris topology. This connection makes clear the relation between our point-set topological approach to choice-free Stone duality, which may be called the hyperspace approach, and a point-free approach to choice-free Stone duality using Stone locales. Unlike Stone’s representation of Boolean algebras via Stone spaces, our choice-free topological representation of Boolean algebras does not show that every Boolean algebra can be represented as a field of sets; but like Stone’s representation, it provides the benefit of a topological perspective on Boolean algebras, only now without choice. In addition to representation, we establish a choice-free dual equivalence between the category of Boolean algebras with Boolean homomorphisms and a subcategory of the category of spectral spaces with spectral maps. We show how this duality can be used to prove some basic facts about Boolean algebras.
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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 (December 1, 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 Boolean algebra. This is done by reinterpreting the aforementioned g(X,Z) as g(Z): B_(2^K)^n→ B_(2^K ), where B_(2^K ) is the free Boolean algebra FB(X_1,X_2…….X_k ), which has K= 2^k atoms, and 2^K elemnets. This paper describes how to unify many digital specifications into a single Boolean equation, suppress unwanted intermediary variables Y, and solve the equation g(Z)=1 for outputs Z (in terms of inputs X) in the absence of any information about Y. The paper uses a novel method for obtaining the parametric general solutions of the ‘big’ Boolean equation g(Z)=1. The parameters used do not belong to B_(2^K ) but they belong to the two-valued Boolean algebra B_2, also known as the switching algebra or propositional algebra. To achieve this, we have to use distinct independent parameters for each asserted atom in the Boole-Shannon expansion of g(Z). The concepts and methods introduced herein are demonsrated via several detailed examples, which cover the most prominent type among basic problems of digital circuit design.
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Bonnet, Robert, and Matatyahu Rubin. "Elementary embedding between countable Boolean algebras." Journal of Symbolic Logic 56, no. 4 (December 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 algebras such that for every n ∈ ω, B(n) ≠ {0}. By Tarski [1949], Tω is complete. Recall that ‹A, < › is partial well-quasi-ordering, it is a partial quasi-ordering and for every {ai, ⃒ i ∈ ω} ⊆ A, there are i < j < ω such that ai ≤ aj. Theorem 2. contains a subset M such that the partial orderings ‹M, ≤ ↾ M› and are isomorphic. ∎ Let M′0 denote the class of all countable Boolean algebras. For B1, B2 ∈ M′0, let B1 ≤′ B2 mean that B1 is embeddable in B2. Remark. ‹M′0, ≤′› is well-quasi-ordered. ∎ This follows from Laver's theorem [1971] that the class of countable linear orderings with the embeddability relation is well-quasi-ordered and the fact that every countable Boolean algebra is isomorphic to a Boolean algebra of a linear ordering.
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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 (December 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 is weakly separable, equivalently that C(K) embeds into l∞. We show that there is a ZFC example of a Boolean algebra (so of a compact space) which satisfies this condition and does not support a separable strictly positive measure. However, we use this property as a tool in a proof which shows that under MA + ¬ CH every atomless ccc Boolean algebra of size < c carries a nonatomic strictly positive measure. Examples are given to show that this result does not hold in ZFC. Finally, we obtain a characterisation of Boolean algebras that carry a strictly positive nonatomic measure in terms of a chain condition, and we draw the conclusion that under MA + ¬ CH every atomless ccc Boolean algebra satisfies this stronger chain condition.
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Dissertations / Theses on the topic "Algebra, Boolean"

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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 proved many properties involving Boolean algebras and related structures. We then expanded our study to more thoroughly developed theory. This comprehensive theory was more abstract and required the use of a different, more universal, notation. We continued examining least upper and greatest lower bounds but extended our knowledge to subalgebras and families of subsets. The notions of cardinality, cellularity, and pairwise disjoint families were investigated, defined, and then used to understand the Erdös-Tarski Theorem. Lastly, this study concluded with the investigation of denseness and incomparability as well as normal forms and the completion of Boolean algebras.
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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 algebras.
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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 action, and other orthomorphism-preserving functions. In addition, we prove a lower bound on the number of orthomorphisms of Zn2 using the equivalence of orthomorphisms to transversals in Latin squares. Lastly, we present a Monte Carlo method for generating orthomorphisms and discuss the results of the implementation.
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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 finite many distinct powers), form a subsemigroup whose structure is studied. There is a natural torsion free quotient D/T whose structure is also investigated. In Chapter 3, the axioms are used to characterize elements s of T in terms of the arithmetic in the subsemigroup generated by the elements that are smaller than s. The characterization is used to determine elements of T that cover a single element. In the last part of Chapter 3, we obtain some sufficient, purely combinatorial conditions for an element to have infinite order.
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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 chapter, we show that if X⊂B is κ—weakly dense for 1 < κ < sat(B), then sup{wd_κ(B):κ < sat(B)} = d(B). In chapter IV, we address the following question: If X is weakly dense in a homogeneous complete Boolean algebra B, does there necessarily exist b € B\{0} such that {x∗b: x ∈ X} is dense in B|b = {c € B: c ≤ b}? We show that the answer is no for collapsing algebras. In chapter V, we give new proofs to some well known results concerning supporting antichains. A direct consequence of these results is the relation c(B) < wd(B), i.e., the weak density of a homogeneous complete Boolean algebra B is at least as big as the cellularity. Also in this chapter, we introduce discernible sets. We prove that a discernible set of cardinality no greater than c(B) cannot be weakly dense. In chapter VI, we prove the main result of this dissertation, i.e., d(B) ≤ min(2^< wd(B),sup{λ^c(B): λ < wd(B)}). In chapter VII, we list some unsolved problems concerning this dissertation.
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Books on the topic "Algebra, Boolean"

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

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

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

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(1990), LMS Durham Symposium. Boolean function complexity. Cambridge: 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. New York, NY: Springer New York, 2009.

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

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Abad, Manuel. Monadic symmetric Boolean algebras. Bahia Blanca, Argentina: INMABB, 1989.

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Pinus, A. G. Constructions of Boolean algebras. Novosibirsk: 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. Amsterdam, Netherlands: North-Holland Pub. Co., 1986.

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

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Book chapters on the topic "Algebra, Boolean"

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Hailperin, Theodore. "Boole’s Algebra Isn’t Boolean Algebra." In A Boole Anthology, 61–77. Dordrecht: 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, 23–50. Basel: 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, 26–61. New York, NY: 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, 45–49. Dordrecht: 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, 168–81. New York, NY: 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, 11–24. Cham: 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, 167–73. Boston, MA: 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, 139. Boston, MA: 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, 143–52. Boca Raton: CRC Press, 2022. http://dx.doi.org/10.1201/9781003316244-6.

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Andonov, Sasho. "Boolean Algebra." In Bowtie Methodology, 59–71. Boca Raton : CRC Press, 2018.: CRC Press, 2017. http://dx.doi.org/10.1201/9781315158853-4.

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Conference papers on the topic "Algebra, Boolean"

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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 computer science through logic gates. The third chapter considers the application of logic gates and various ex- amples from information technology in teaching mathematics, so that students can more easily understand Boolean algebra and logical operations.
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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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10

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"

1

McCune, W. Single axioms for Boolean algebra. Office of Scientific and Technical Information (OSTI), June 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), June 2000. http://dx.doi.org/10.2172/764209.

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Barnett, Janet Heine. Applications of Boolean Algebra: Claude Shannon and Circuit Design. Washington, DC: The MAA Mathematical Sciences Digital Library, July 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. Washington, DC: The MAA Mathematical Sciences Digital Library, July 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. Washington, DC: The MAA Mathematical Sciences Digital Library, July 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, both without and with TBoxes.
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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, but is not restricted to them. The known fusion decidability results for modal logics are instances of our approach. However, even for equational theories induced by modal logics our results are more general since they are not restricted to so-called normal modal logics.
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