Relevant bibliographies by topics / Boolean

Contents

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

Academic literature on the topic 'Boolean'

Author: Grafiati
Published: 4 June 2021
Last updated: 15 June 2025

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Journal articles on the topic "Boolean"

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Chernoskutov, Yu Yu. "On the Syllogistic of G. Boole." Discourse 7, no. 2 (2021): 5–15. http://dx.doi.org/10.32603/2412-8562-2021-7-2-5-15.

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Introduction. This article focuses on the investigation of Boole’s theory of categorical syllogism, exposed in his book “The Mathematical analysis of Logic”. That part of Boolean legacy has been neglected in the prevailed investigations on the history of logic; the latter provides the novelty of the work presented.Methodology and sources. The formal reconstruction of the methods of algebraic presentation of categorical syllogism, as it is exposed in the original work of Boole, is conducted. The character of Boolean methods is investigated in the interconnections with the principles of symbolic algebra on the one hand, and with the principles of signification, taken from R. Whately, on the other hand. The approaches to signification, grounding the syllogistic theories of Boole and Brentano, are analyzed in comparison, wherefrom we explain the reasons why the results of those theories are different so much.Results and discussion. It is demonstrated here that Boole has borrowed the principles of signification from the Whately’s book “The Elements of Logic”. The interpreting the content of the terms as classes, being combined with methods of symbolic algebra, has determined the core features of Boolean syllogism theory and its unexpected results. In contrast to Whately, Boole conduct the approach to ultimate ends, overcoming the restrictions imposed by Aristotelean doctrine. In particular, he neglects the distinction of subject and predicate among the terms of proposition, the order of premises, and provide the possibility to draw conclusions with negative terms. At the same time Boole missed that the forms of inference, parallel to Bramantip and Fresison, are legitimate forms in his system. In spite of the apparent affinities between the Boolean and Brentanian theories of judgment, the syllogistics of Boole appeared to be more flexible. The drawing of particular conclusion from universal premises is allowable in Boolean theory, but not in Brentanian one; besides, in his theory is allowable the drawing of conclusion from two negative premises, which is prohibited in Aristotelian syllogistic.Conclusion. Boole consistently interpreted signification of terms as classes; being combine with methods symbolic algebra it led to very flexible syllogism theory with rich results.
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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 systems exact for the boolean abstraction while preserving the solutions over the positive reals. The rewriting algorithm is based on the elementary modes of the linear equation system. The computation of the elementary modes may require exponential time in the worst case, but is often feasible in practice with freely available tools. For exact linear equation systems, we can compute the boolean abstraction by finite domain constraint programming. This yields a solution of the initial problem that is often feasible in practice. Our exact rewriting algorithm has two further applications. Firstly, it can be used to compute the sign abstraction of linear equation systems over the reals, as needed for analyzing function programs with linear arithmetics. Secondly, it can be applied to compute the difference abstraction of a linear equation system as used in change prediction algorithms for flux networks in systems biology.
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Huang, Jing Lian, Su Duo Li, Yong Liu, and Ke Yan Deng. "On Analysis and Judgment of Balance for Boolean Functions by E-Derivative." Applied Mechanics and Materials 643 (September 2014): 130–35. http://dx.doi.org/10.4028/www.scientific.net/amm.643.130.

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Using the derivative of the Boolean function and the e-derivative defined by ourselves as research tools and deeply into the internal structure of Boolean, we study the issues of the analysis and judgment of balance for Boolean functions. We get that the linear functions and the nonzero derivative of the product of two linear functions are balanced functions, and the product of two linear functions are not balanced functions. We also obtain the quadratic homogeneous Booleans are not all balanced function. Besides, we deduce the theorem which determine the sum of linear function and balanced function whether it is a balanced function. What is more, the features of balance of Boolean functions can be reflected easily and effectively by e-derivative.
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De Villiers, Michael D. "Teaching Modeling and Axiomatization with Boolean Algebra." Mathematics Teacher 80, no. 7 (1987): 528–32. http://dx.doi.org/10.5951/mt.80.7.0528.

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Traditionally, Boolean algebra is largely taught in connection with computer programming courses, logic, or set theory. Since Boolean algebra arose from George Boole's application of algebraic principles to the study of logic in 1854, this approach would seem natural.
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Chajda, I., and M. Kotrle. "Boolean semirings." Czechoslovak Mathematical Journal 44, no. 4 (1994): 763–67. http://dx.doi.org/10.21136/cmj.1994.128495.

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Madsen, Magnus, Jaco van de Pol, and Troels Henriksen. "Fast and Efficient Boolean Unification for Hindley-Milner-Style Type and Effect Systems." Proceedings of the ACM on Programming Languages 7, OOPSLA2 (2023): 516–43. http://dx.doi.org/10.1145/3622816.

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As type and effect systems become more expressive there is an increasing need for efficient type inference. We consider a polymorphic effect system based on Boolean formulas where inference requires Boolean unification. Since Boolean unification involves semantic equivalence, conventional syntax-driven unification is insufficient. At the same time, existing Boolean unification techniques are ill-suited for type inference. We propose a hybrid algorithm for solving Boolean unification queries based on Boole’s Successive Variable Elimination (SVE) algorithm. The proposed approach builds on several key observations regarding the Boolean unification queries encountered in practice, including: (i) most queries are simple, (ii) most queries involve a few flexible variables, (iii) queries are likely to repeat due similar programming patterns, and (iv) there is a long tail of complex queries. We exploit these observations to implement several strategies for formula minimization, including ones based on tabling and binary decision diagrams. We implement the new hybrid approach in the Flix programming language. Experimental results show that by reducing the overhead of Boolean unification, the compilation throughput increases from 8,580 lines/sec to 15,917 lines/sec corresponding to a 1.8x speed-up. Further, the overhead on type and effect inference time is only 16% which corresponds to an overhead of less than 7% on total compilation time. We study the hybrid approach and demonstrate that each design choice improves performance.
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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 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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Wehrung, Friedrich. "Boolean universes above Boolean models." Journal of Symbolic Logic 58, no. 4 (1993): 1219–50. http://dx.doi.org/10.2307/2275140.

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AbstractWe establish several first- or second-order properties of models of first-order theories by considering their elements as atoms of a new universe of set theory and by extending naturally any structure of Boolean model on the atoms to the whole universe. For example, complete f-rings are “boundedly algebraically compact” in the language (+, −, ·, ∧, ∨, ≤), and the positive cone of a complete l-group with infinity adjoined is algebraically compact in the language (+, ∨, ≤). We also give an example with any first-order language. The proofs can be translated into “naive set theory” in a uniform way.
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Studenic, Paul, David Felson, Maarten de Wit, et al. "Testing different thresholds for patient global assessment in defining remission for rheumatoid arthritis: are the current ACR/EULAR Boolean criteria optimal?" Annals of the Rheumatic Diseases 79, no. 4 (2020): 445–52. http://dx.doi.org/10.1136/annrheumdis-2019-216529.

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ObjectivesThis study aimed to evaluate different patient global assessment (PGA) cut-offs required in the American College of Rheumatology/European League Against Rheumatism (ACR/EULAR) Boolean remission definition for their utility in rheumatoid arthritis (RA).MethodsWe used data from six randomised controlled trials in early and established RA. We increased the threshold for the 0–10 score for PGA gradually from 1 to 3 in steps of 0.5 (Boolean1.5 to Boolean3.0) and omitted PGA completely (BooleanX) at 6 and 12 months. Agreement with the index-based (Simplified Disease Activity Index (SDAI)) remission definition was analysed using kappa, recursive partitioning (classification and regression tree (CART)) and receiver operating characteristics. The impact of achieving each definition on functional and radiographic outcomes after 1 year was explored.ResultsData from 1680 patients with early RA and 920 patients with established RA were included. The proportion of patients achieving Boolean remission increased with higher thresholds for PGA from 12.4% to 19.7% in early and 5.9% to 12.3% in established RA at 6 months. Best agreement with SDAI remission occurred at PGA cut-offs of 1.5 and 2.0, while agreement decreased with higher PGA (CART: optimal agreement at PGA≤1.6 cm; sensitivity of PGA≤1.5 95%). Changing PGA thresholds at 6 months did not affect radiographic progression at 12 months (mean ꙙsmTSS for Boolean, 1.5, 2.0, 2.5, 3.0, BooleanX: 0.35±5.4, 0.38±5.14, 0.41±5.1, 0.37±4.9, 0.34±4.9, 0.27±4.7). However, the proportion attaining HAQ≤0.5 was 90.2%, 87.9%, 85.2%, 81.1%, 80.7% and 73.1% for the respective Boolean definitions.ConclusionIncreasing the PGA cut-off to 1.5 cm would provide high consistency between Boolean with the index-based remission; the integer cut-off of 2.0 cm performed similarly.
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Kadioglu, Serdar, Elton Yechao Zhu, Gili Rosenberg, et al. "BoolXAI: Explainable AI Using Expressive Boolean Formulas." Proceedings of the AAAI Conference on Artificial Intelligence 39, no. 28 (2025): 28900–28906. https://doi.org/10.1609/aaai.v39i28.35157.

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In this tool paper, we design, develop, and release BoolXAI, an interpretable machine learning classification approach for Explainable AI (XAI) based on expressive Boolean formulas. The Boolean formula defines a logical rule with tunable complexity according to which input data are classified. Beyond the classical conjunction and disjunction, BoolXAI offers expressive operators such as AtLeast, AtMost, and Choose and their parameterization. This provides higher expressiveness compared to rigid rules- and tree-based approaches. We show how to train BoolXAI classifiers effectively using native local optimization to search the space of feasible formulas. We provide illustrative results on several well-known public benchmarks that demonstrate the competitive nature of our approach compared to existing methods. Our work is embodied in the open-source BoolXAI library with a high-level user interface to serve researchers and practitioners. BoolXAI can be used either as a standalone interpretable classifier or for post-hoc explanations of other black-box models or observed behavior. We highlight several desirable benefits of our tool, especially in industrial settings where rapid experimentation, reusability, reproducibility, deployment, and maintenance are of great interest. Finally, we showcase a deployed service powered by BoolXAI as an enterprise application.
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Dissertations / Theses on the topic "Boolean"

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Fish, Washiela. "Boolean ultrapowers." Master's thesis, University of Cape Town, 2000. http://hdl.handle.net/11427/13892.

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Bibliography: leaves 121-122.<br>The Boolean ultrapower construction is a generalisation of the ordinary ultrapower construction in that an arbitrary complete Boolean algebra replaces the customary powerset Boolean algebra. B. Koppelberg and S. Koppelberg [1976] show that the class of ordinary ultrapowers is properly contained in the class of Boolean ultrapowers thereby justifying the development of a theory for Boolean ultrapowers. This thesis is an exploration into the strategies whereby and the conditions under which aspects of the theory of ordinary ultrapowers can be extended to the theory of Boolean ultrapowers. Mansfield [1971] shows that a finitely iterated Boolean ultrapower is isomorphic to a single Boolean ultrapower under certain conditions. Using a different approach and under somewhat different conditions, Ouwehand and Rose [1998] show that the result also holds for K-bounded Boolean ultrapowers. Mansfield [1971] also proves a Boolean version of the Keisler-Shelah theorem. By redefining the notion of a K-good ultrafilter on a Boolean algebra, Benda [1974] obtains a complete generalisation of a theorem of Keisler which states that an ultrapower is K-saturated iff the ultrafilter is K-good. Potthoff [1974] defines the notion of a limit Boolean ultrapower and shows that, as is the case for ordinary ultrapowers, the complete extensions of a model are characterised by its limit Boolean ultrapowers. Upon the discovery by Frayne, Morel and Scott [1962] of an ultrapower of a simple group which is not simple, Burris and Jeffers [1978] investigate necessary and sufficient conditions for a Boolean ultrapower to be simple, or subdirectly irreducible, provided that the language is countable. Finally, Jipsen, Pinus and Rose [2000] extend the notion of the Rudin-Keisler ordering to ultrafilters on complete Boolean algebras, and prove that by using this definition, Blass' Characterisation Theorem can be generalised for Boolean ultrapowers.
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Van, Name Joseph. "Boolean Partition Algebras." Thesis, University of South Florida, 2013. http://pqdtopen.proquest.com/#viewpdf?dispub=3560193.

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<p>A Boolean partition algebra is a pair (<i>B</i>, <i>F </i>) where <i>B</i> is a Boolean algebra and <i>F</i> is a filter on the semilattice of partitions of <i>B</i> where [special characters omitted] <i>F</i> = <i>B</i> \ {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.</p>
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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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Shen, Amelia H. (Amelia Huimin). "Probabilistic representation and manipulation of Boolean functions using free Boolean diagrams." Thesis, Massachusetts Institute of Technology, 1994. http://hdl.handle.net/1721.1/34087.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1994.<br>Includes bibliographical references (p. 145-149).<br>by Amelia Huimin Shen.<br>Ph.D.
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Skelley, Alan. "Relating the PSPACE reasoning power of Boolean Programs and quantified Boolean formulas." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp01/MQ53391.pdf.

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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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Karlsson, Fredrik. "Dynamics in Boolean Networks." Thesis, Linköping University, Department of Science and Technology, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-2888.

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<p>In this thesis several random Boolean networks are simulated. Both completely computer generated network and models for biological networks are simulated. Several different tools are used to gain knowledge about the robustness. These tools are Derrida plots, noise analysis and mean probability for canalizing rules. Some simulations on how entropy works as an indicator on if a network is robust are also included. The noise analysis works by measuring the hamming distance between the state of the network when noise is applied and when no noise is applied. For many of the simulated networks two types of rules are applied: nested canalizing and flat distributed rules. The computer generated networks consists of two types of networks: scale-free and ER-networks. One of the conclusions in this report is that nested canalizing rules are often more robust than flat distributed rules. Another conclusion is that the mean probability for canalizing rules has, for flat distributed rules, a very dominating effect on if the network is robust or not. Yet another conclusion is that the probability distribution for indegrees, for flat distributed rules, has a strong effect on if a network is robust due to the connection between the probability distribution for indegrees and the mean probability for canalizing rules.</p>
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Ghanbarnejad, Fakhteh. "Perturbations in Boolean Networks." Doctoral thesis, Universitätsbibliothek Leipzig, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-96825.

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Boolean networks are coarse-grained models of the regulatory dynamics that controls the survival and proliferation of a living cell. The dynamics is time- and state-discrete. This Boolean abstraction assumes that small differences in concentration levels are irrelevant; and the binary distinction of a low or a high concentration of each biomolecule is sufficient to capture the dynamics. In this work, we briefly introduce the gene regulatory models, where with the advent of system-specific Boolean models, new conceptual questions and analytical and numerical challenges arise. In particular, the response of the system to external intervention presents a novel area of research. Thus first we investigate how to quantify a node\\\'s individual impact on dynamics in a more detailed manner than an averaging against all eligible perturbations. Since each node now represents a specific biochemical entity, it is the subject of our interest. The prediction of nodes\\\' dynamical impacts from the model may be compared to the empirical data from biological experiments. Then we develop a hybrid model that incorporates both continuous and discrete random Boolean networks to compare the reaction of the dynamics against small as well as flip perturbations in different regimes. We show that the chaotic behaviour disappears in high sensitive Boolean ensembles with respect to continuous small fluctuations in contrast to the flipping. Finally, we discuss the role of distributing delays in stabilizing of the Boolean dynamics against noise. These studies are expected to trigger additional experiments and lead to improvement of models in gene regulatory dynamics.
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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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Boris, Šobot. "Games on Boolean algebras." Phd thesis, Univerzitet u Novom Sadu, Prirodno-matematički fakultet u Novom Sadu, 2009. http://dx.doi.org/10.2298/NS20090907SOBOT.

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The method of forcing is widely used in set theory to obtain&nbsp;various consistency proofs. Complete Boolean algebras play the main role&nbsp;in applications of forcing. Therefore it is useful to define games on Boolean&nbsp;algebras that characterize their properties important for the method. The&nbsp;most investigated game is Jech&rsquo;s distributivity game, such that the first&nbsp;player has the winning strategy iff the algebra is not (&omega;, 2)-distributive.&nbsp;We define another game characterizing the collapsing of the continuum to&nbsp;&omega;, prove several sufficient conditions for the second player to have a winning&nbsp;strategy, and obtain a Boolean algebra on which the game is undetermined.&nbsp;<br>Forsing je metod &scaron;iroko kori&scaron;ćen u teoriji skupova za dokaze konsistentnosti. Kompletne&nbsp; Bulove algebre igraju glavnu ulogu u primenama forsinga. Stoga je korisno definisati igre na Bulovim algebrama koje karakteri&scaron;u njihove osobine od značaja za taj metod. Najbolje proučena je Jehova igra, koja ima osobinu da prvi igrač ima pobedničku strategiju akko algebra nije (&omega;, 2)-distributivna. U tezi defini&scaron;emo jo&scaron; jednu igru, koja karakteri&scaron;e kolaps kontinuuma na &omega;, dokazujemo nekoliko dovoljnih uslova da bi drugi igra&scaron; imao pobedničku strategiju, i konstrui&scaron;emo Bulovu algebru na kojoj je igra neodređena.
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Books on the topic "Boolean"

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Brown, Frank Markham. Boolean Reasoning. Springer US, 1990. http://dx.doi.org/10.1007/978-1-4757-2078-5.

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Schneeweiss, Winfrid G. Boolean Functions. Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-642-45638-1.

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Vlad, Serban E., ed. Boolean Functions. John Wiley & Sons, Inc., 2019. http://dx.doi.org/10.1002/9781119517528.

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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, 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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Steinbach, Bernd, and Christian Posthoff. Boolean Differential Calculus. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-031-79892-4.

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Lam, William K. C., and Robert K. Brayton. Timed Boolean Functions. Springer US, 1994. http://dx.doi.org/10.1007/978-1-4615-2688-9.

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Lam, Tak-Kei, Wai-Chung Tang, Xing Wei, Yi Diao, and David Yu-LiangWu. Boolean Circuit Rewiring. John Wiley & Sons Singapore Pte. Ltd, 2016. http://dx.doi.org/10.1002/9781118750124.

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Book chapters on the topic "Boolean"

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Weik, Martin H. "Boolean." In Computer Science and Communications Dictionary. Springer US, 2000. http://dx.doi.org/10.1007/1-4020-0613-6_1762.

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Schneeweiss, Winfrid G. "Boolean Functions Without Boolean Operators." In Boolean Functions. Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-642-45638-1_7.

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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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Rodríguez, Andoni, and César Sánchez. "Boolean Abstractions for Realizability Modulo Theories." In Computer Aided Verification. Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-37709-9_15.

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AbstractIn this paper, we address the problem of the (reactive) realizability of specifications of theories richer than Booleans, including arithmetic theories. Our approach transforms theory specifications into purely Boolean specifications by (1) substituting theory literals by Boolean variables, and (2) computing an additional Boolean requirement that captures the dependencies between the new variables imposed by the literals. The resulting specification can be passed to existing Boolean off-the-shelf realizability tools, and is realizable if and only if the original specification is realizable. The first contribution is a brute-force version of our method, which requires a number of SMT queries that is doubly exponential in the number of input literals. Then, we present a faster method that exploits a nested encoding of the search for the extra requirement and uses SAT solving for faster traversing the search space and uses SMT queries internally. Another contribution is a prototype in Z3-Python. Finally, we report an empirical evaluation using specifications inspired in real industrial cases. To the best of our knowledge, this is the first method that succeeds in non-Boolean LTL realizability.
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Brown, Frank Markham. "Boolean Algebras." In Boolean Reasoning. Springer US, 1990. http://dx.doi.org/10.1007/978-1-4757-2078-5_2.

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Brown, Frank Markham. "Boolean Analysis." In Boolean Reasoning. Springer US, 1990. http://dx.doi.org/10.1007/978-1-4757-2078-5_4.

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Brown, Frank Markham. "Boolean Identification." In Boolean Reasoning. Springer US, 1990. http://dx.doi.org/10.1007/978-1-4757-2078-5_8.

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Givant, Steven. "Boolean Algebras and Boolean Spaces." In Undergraduate Texts in Mathematics. Springer New York, 2009. http://dx.doi.org/10.1007/978-0-387-68436-9_34.

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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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Brown, Frank Markham. "Fundamental Concepts." In Boolean Reasoning. Springer US, 1990. http://dx.doi.org/10.1007/978-1-4757-2078-5_1.

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Conference papers on the topic "Boolean"

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Kolomvakis, Christos, Arnaud Vandaele, and Nicolas Gillis. "Boolean Matrix Tri-Factorization." In ICASSP 2025 - 2025 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2025. https://doi.org/10.1109/icassp49660.2025.10889808.

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Liu, Qiang, Mahdi Soleymani, and Hessam Mahdavifar. "Boolean matrix compressed sensing." In ICASSP 2025 - 2025 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2025. https://doi.org/10.1109/icassp49660.2025.10888788.

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Zhang, Zhen, Seung-won Hwang, Kevin Chen-Chuan Chang, Min Wang, Christian A. Lang, and Yuan-chi Chang. "Boolean + ranking." In the 2006 ACM SIGMOD international conference. ACM Press, 2006. http://dx.doi.org/10.1145/1142473.1142515.

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McAllester, David, and Ramin Zabih. "Boolean classes." In Conference proceedings. ACM Press, 1986. http://dx.doi.org/10.1145/28697.28740.

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Sharad, Mrigank, Charles Augustine, and Kaushik Roy. "Boolean and non-Boolean computation with spin devices." In 2012 IEEE International Electron Devices Meeting (IEDM). IEEE, 2012. http://dx.doi.org/10.1109/iedm.2012.6479026.

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Iorgulescu, Afrodita. "Quasi-i-Boolean algebras vs. quasi-m Boolean algebras." In Proceedings of the 2019 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology (EUSFLAT 2019). Atlantis Press, 2019. http://dx.doi.org/10.2991/eusflat-19.2019.48.

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Lin, Pey-Chang Kent, and Sunil P. Khatri. "Determining gene function in boolean networks using boolean satisfiability." In 2012 IEEE International Workshop on Genomic Signal Processing and Statistics (GENSIPS). IEEE, 2012. http://dx.doi.org/10.1109/gensips.2012.6507757.

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Shukla, N. "Emerging Hardware Substrates for Boolean and Non-Boolean Computing." In 2018 International Conference on Solid State Devices and Materials. The Japan Society of Applied Physics, 2018. http://dx.doi.org/10.7567/ssdm.2018.j-8-01.

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Huo, Jiwen, and Wm Cowan. "Comprehending Boolean queries." In the 5th symposium. ACM Press, 2008. http://dx.doi.org/10.1145/1394281.1394314.

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Miettinen, Pauli. "Boolean Tensor Factorizations." In 2011 IEEE 11th International Conference on Data Mining (ICDM). IEEE, 2011. http://dx.doi.org/10.1109/icdm.2011.28.

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Reports on the topic "Boolean"

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Prokopyev, Oleg. Stochastic Pseudo-Boolean Optimization. Defense Technical Information Center, 2011. http://dx.doi.org/10.21236/ada564073.

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Schimanski, Nichole. Orthomorphisms of Boolean Groups. Portland State University Library, 2000. http://dx.doi.org/10.15760/etd.3097.

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Lutz, Carsten, and Ulrike Sattler. The Complexity of Reasoning with Boolean Modal Logics (Extended Version). Aachen University of Technology, 1999. http://dx.doi.org/10.25368/2022.105.

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Abstract:
Since Modal Logics are an extension of Propositional Logic, they provide Boolean operators for constructing complex formulae. However, most Modal Logics do not admit Boolean operators for constructing complex modal parameters to be used in the box and diamond operators. This asymmetry is not present in Boolean Modal Logics, in which box and diamond quantify over arbitrary Boolean combinations of atomic model parameters.
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Lipscomb, Stephen, and Chris Dupilka. Inverse Semigroups and Boolean Matrices,. Defense Technical Information Center, 1996. http://dx.doi.org/10.21236/ada312447.

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Chen, Crystal, Charlotte Ellison, Zachary Roth, and Mackenzie Simper. Boolean decomposition of spatiotemporal tensors. Engineer Research and Development Center (U.S.), 2019. http://dx.doi.org/10.21079/11681/33849.

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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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Bryan, Randal E., and Miroslav N. Velev. Boolean Satisfiability with Transitivity Constraints. Defense Technical Information Center, 2000. http://dx.doi.org/10.21236/ada382689.

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Dukes, Michael A., and Frank M. Brown. Proving Boolean Equivalence with Prolog. Defense Technical Information Center, 1990. http://dx.doi.org/10.21236/ada221766.

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Cherupally, Sai Kiran. Hierarchical Random Boolean Network Reservoirs. Portland State University Library, 2000. http://dx.doi.org/10.15760/etd.6238.

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Stanica, Pantelimon, Thor Martinsen, Sugata Gangopadhyay, and Brajesh K. Singh. Bent and Generalized Bent Boolean Functions. Defense Technical Information Center, 2012. http://dx.doi.org/10.21236/ada574574.

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