Relevant bibliographies by topics / Algorithm algebra

Academic literature on the topic 'Algorithm algebra'

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Published: 30 May 2022
Last updated: 31 May 2022

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Journal articles on the topic "Algorithm algebra"

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Bancerek, Grzegorz. "Analysis of Algorithms: An Example of a Sort Algorithm." Formalized Mathematics 21, no. 1 (January 1, 2013): 1–23. http://dx.doi.org/10.2478/forma-2013-0001.

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INAMI, T., Y. MATSUO, and I. YAMANAKA. "EXTENDED CONFORMAL ALGEBRA WITH N=2 SUPERSYMMETRY." International Journal of Modern Physics A 05, no. 23 (December 10, 1990): 4441–67. http://dx.doi.org/10.1142/s0217751x90001860.

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We construct an N=2 supersymmetric extension of Zamolodchikov’s W algebra. The generators of this extended conformal algebra consist of the stress-tensor superfield and a pair of chiral currents [Formula: see text] of integer or half-integer spin Δ and opposite U(I) charges ±τ. The algorithm for deriving the operator product algebra [Formula: see text] is given for general Δ and the algebra is worked out explicitly for Δ=3/2. The N=2 super-W algebra has an interesting feature not shared by other conformal algebras, i.e. it has two types of algebra—short and long algebras.
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Vasyluk, Andrii, and Taras Basyuk. "Synthesis System Оf Algebra Algorithms Formulas." Vìsnik Nacìonalʹnogo unìversitetu "Lʹvìvsʹka polìtehnìka". Serìâ Ìnformacìjnì sistemi ta merežì 9 (June 10, 2021): 11–22. http://dx.doi.org/10.23939/sisn2021.09.011.

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In the article the authors have developed a mathematical support for the process of generating subject unitherms of formulas of algebra of algorithms. The analysis of features of construction of formulas of algebra of algorithms as a result of which it was found out, that today, subsystems with realization of processes of generation of subject unitherms on the basis of abstract unitherms with the subsequent adaptation of formulas are not realized in known systems that served as stimulus to intellectual analysis formulas of algebra of algorithms. It is described that the synthesis of algebra formulas of algorithms, and especially the generation of subject unitherms on the basis of abstract ones is an extremely complex and laborious process. Since all elements of the formula are interconnected, all changes in the algorithm’s formula affect its structure. Therefore, this is the main reason for the complexity of the described processes. One aspect of the synthesis of the formulas of the algebra of algorithms is the process of generating subject unitherms based on abstract unitherms. The signs of operations of the algebra of algorithms are briefly described. Mathematical support of the process of synthesis of algorithm algebra formulas is developed, which takes into account vertical and horizontal orientation and type of algorithm algebra formula: text unitherm, sequencing operation, elimination operation, parallel operation and corresponding cyclic sequencing operations, elimination and parallelization, as well as geometric parameters. The process of generating subject unitherms on the basis of abstract ones is previously described. The list of necessary eliminations and sequences for the synthesis of the corresponding formulas is determined. According to the properties of the signs of operations of the algebra of algorithms, the synthesized formulas of the algorithms are minimized by the number of unitherms. Also, in accordance with the properties of the formulas of the algorithms of algebra, the corresponding unitherms are taken out as signs of operations, as a result of which the formula of the algorithm for the synthesis of algorithm formulas is obtained taking into account the generation of subject unitherms based on abstract unitherms.
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Mei, Xu Shi. "Research on Vector Algebra Algorithm of Network Coding." Applied Mechanics and Materials 416-417 (September 2013): 1614–18. http://dx.doi.org/10.4028/www.scientific.net/amm.416-417.1614.

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The vector algebra algorithm has been conducted in - depth study, through the vector algorithm to adjust the conversion of vector data and raster data, it can finally realize the quantization scheme of vector algebra algorithms that are applied to network coding, vector algebra algorithm will be conducive to the network and retrieval analysis, the graphical display also has good quality and high precision. At the same time, data structure is simple and easy to spatial analysis and surface modeling.
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FLAUT, CRISTINA, and DIANA SAVIN. "Some examples of division symbol algebras of degree 3 and 5." Carpathian Journal of Mathematics 31, no. 2 (2015): 197–204. http://dx.doi.org/10.37193/cjm.2015.02.07.

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In this paper we provide an algorithm to compute the product between two elements in a symbol algebra of degree n and we find an octonion algebra (in general, without division) in a symbol algebra of degree three. Moreover, using MAGMA software, we will provide some examples of division symbol algebras of degree 3 and of degree 5.
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Casas, J. M., M. Ladra, B. A. Omirov, and U. A. Rozikov. "On Evolution Algebras." Algebra Colloquium 21, no. 02 (April 11, 2014): 331–42. http://dx.doi.org/10.1142/s1005386714000285.

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The structural constants of an evolution algebra are given by a quadratic matrix. In this work we establish an equivalence between nil, right nilpotent evolution algebras and evolution algebras defined by upper triangular matrices. The classification of 2-dimensional complex evolution algebras is obtained. For an evolution algebra with a special form of the matrix, we describe all its isomorphisms and their compositions. We construct an algorithm running under Mathematica which decides if two finite dimensional evolution algebras are isomorphic.
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RIZELL, GEORGIOS DIMITROGLOU. "Nontriviality results for the characteristic algebra of a DGA." Mathematical Proceedings of the Cambridge Philosophical Society 162, no. 3 (July 28, 2016): 419–33. http://dx.doi.org/10.1017/s0305004116000645.

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AbstractAssume that we are given a semifree noncommutative differential graded algebra (DGA for short) whose differential respects an action filtration. We show that the canonical unital algebra map from the homology of the DGA to its characteristic algebra, i.e. the quotient of the underlying algebra by the two-sided ideal generated by the boundaries, is a monomorphism. The main tool that we use is the weak division algorithm in free noncommutative algebras due to P. Cohn.
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NURAKUNOV, ANVAR M., and MICHAŁ M. STRONKOWSKI. "PROFINITENESS IN FINITELY GENERATED VARIETIES IS UNDECIDABLE." Journal of Symbolic Logic 83, no. 04 (December 2018): 1566–78. http://dx.doi.org/10.1017/jsl.2017.89.

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AbstractProfinite algebras are exactly those that are isomorphic to inverse limits of finite algebras. Such algebras are naturally equipped with Boolean topologies. A variety ${\cal V}$ is standard if every Boolean topological algebra with the algebraic reduct in ${\cal V}$ is profinite.We show that there is no algorithm which takes as input a finite algebra A of a finite type and decide whether the variety $V\left( {\bf{A}} \right)$ generated by A is standard. We also show the undecidability of some related properties. In particular, we solve a problem posed by Clark, Davey, Freese, and Jackson.We accomplish this by combining two results. The first one is Moore’s theorem saying that there is no algorithm which takes as input a finite algebra A of a finite type and decides whether $V\left( {\bf{A}} \right)$ has definable principal subcongruences. The second is our result saying that possessing definable principal subcongruences yields possessing finitely determined syntactic congruences for varieties. The latter property is known to yield standardness.
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Chen, Yuqun. "Gröbner–Shirshov Bases for Extensions of Algebras." Algebra Colloquium 16, no. 02 (June 2009): 283–92. http://dx.doi.org/10.1142/s1005386709000285.

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An algebra [Formula: see text] is called an extension of the algebra M by B if M2 = 0, M is an ideal of [Formula: see text] and [Formula: see text] as algebras. In this paper, by using Gröbner–Shirshov bases, we characterize completely the extensions of M by B. An algorithm to find the conditions of an algebra A to be an extension of M by B is obtained.
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Vejdemo-Johansson, Mikael. "Blackbox computation of A ∞-algebras." gmj 17, no. 2 (June 2010): 391–404. http://dx.doi.org/10.1515/gmj.2010.005.

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Abstract Kadeishvili's proof of theminimality theorem [T. Kadeishvili, On the homology theory of fiber spaces, Russ. Math. Surv. 35:3 (1980), 231–238] induces an algorithm for the inductive computation of an A ∞-algebra structure on the homology of a dg-algebra. In this paper, we prove that for one class of dg-algebras, the resulting computation will generate a complete A ∞-algebra structure after a finite amount of computational work.
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Dissertations / Theses on the topic "Algorithm algebra"

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Maust, Reid S. "Optimal power flow using a genetic algorithm and linear algebra." Morgantown, W. Va. : [West Virginia University Libraries], 1999. http://etd.wvu.edu/templates/showETD.cfm?recnum=1163.

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Thesis (Ph. D.)--West Virginia University, 1999.
Title from document title page. Document formatted into pages; contains vi, 91 p. : ill. Vita. Includes abstract. Includes bibliographical references (p. 41-42).
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Delaplace, Claire. "Algorithmes d'algèbre linéaire pour la cryptographie." Thesis, Rennes 1, 2018. http://www.theses.fr/2018REN1S045/document.

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Dans cette thèse, nous discutons d’aspects algorithmiques de trois différents problèmes, en lien avec la cryptographie. La première partie est consacrée à l’algèbre linéaire creuse. Nous y présentons un nouvel algorithme de pivot de Gauss pour matrices creuses à coefficients exacts, ainsi qu’une nouvelle heuristique de sélection de pivots, qui rend l’entière procédure particulièrement efficace dans certains cas. La deuxième partie porte sur une variante du problème des anniversaires, avec trois listes. Ce problème, que nous appelons problème 3XOR, consiste intuitivement à trouver trois chaînes de caractères uniformément aléatoires de longueur fixée, telles que leur XOR soit la chaîne nulle. Nous discutons des considérations pratiques qui émanent de ce problème et proposons un nouvel algorithme plus rapide à la fois en théorie et en pratique que les précédents. La troisième partie est en lien avec le problème learning with errors (LWE). Ce problème est connu pour être l’un des principaux problèmes difficiles sur lesquels repose la cryptographie à base de réseaux euclidiens. Nous introduisons d’abord un générateur pseudo-aléatoire, basé sur la variante dé-randomisée learning with rounding de LWE, dont le temps d’évaluation est comparable avec celui d’AES. Dans un second temps, nous présentons une variante de LWE sur l’anneau des entiers. Nous montrerons que dans ce cas le problème est facile à résoudre et nous proposons une application intéressante en re-visitant une attaque par canaux auxiliaires contre le schéma de signature BLISS
In this thesis, we discuss algorithmic aspects of three different problems, related to cryptography. The first part is devoted to sparse linear algebra. We present a new Gaussian elimination algorithm for sparse matrices whose coefficients are exact, along with a new pivots selection heuristic, which make the whole procedure particularly efficient in some cases. The second part treats with a variant of the Birthday Problem with three lists. This problem, which we call 3XOR problem, intuitively consists in finding three uniformly random bit-strings of fixed length, such that their XOR is the zero string. We discuss practical considerations arising from this problem, and propose a new algorithm which is faster in theory as well as in practice than previous ones. The third part is related to the learning with errors (LWE) problem. This problem is known for being one of the main hard problems on which lattice-based cryptography relies. We first introduce a pseudorandom generator, based on the de-randomised learning with rounding variant of LWE, whose running time is competitive with AES. Second, we present a variant of LWE over the ring of integers. We show that in this case the problem is easier to solve, and we propose an interesting application, revisiting a side-channel attack against the BLISS signature scheme
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Abrahamsson, Olle. "A Gröbner basis algorithm for fast encoding of Reed-Müller codes." Thesis, Linköpings universitet, Matematik och tillämpad matematik, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-132429.

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In this thesis the relationship between Gröbner bases and algebraic coding theory is investigated, and especially applications towards linear codes, with Reed-Müller codes as an illustrative example. We prove that each linear code can be described as a binomial ideal of a polynomial ring, and that a systematic encoding algorithm for such codes is given by the remainder of the information word computed with respect to the reduced Gröbner basis. Finally we show how to apply the representation of a code by its corresponding polynomial ring ideal to construct a class of codes containing the so called primitive Reed-Müller codes, with a few examples of this result.
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Böhm, Josef. "Linking Geometry, Algebra and Calculus with GeoGebra." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79488.

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GeoGebra is a free, open-source, and multi-platform software that combines dynamic geometry, algebra and calculus in one easy-to-use package. Students from middle-school to university can use it in classrooms and at home. In this workshop, we will introduce the features of GeoGebra with a special focus on not very common applications of a dynamic geometry program. We will inform about plans for developing training and research networks connected to GeoGebra. We can expect that at the time of the conference a spreadsheet will be integrated into GeoGebra which offers new ways teaching mathematics using the interplay between the features of a spreadsheet and the objects of dynamic geometry.
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Vora, Rohit H. "An Algorithm for multi-output Boolean logic minimization." Thesis, Virginia Tech, 1987. http://hdl.handle.net/10919/43829.

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A new algorithm is presented for a guaranteed absolute minimal solution to the problem of Boolean Logic Minimization in its most generalized form of multi-output function with arbitrary cost criterion. The proposed algorithm is shown to be tighter than the Quine-McCluskey method in its ability to eliminate redundant prime implicants, making it possible to simplify the cyclic tables. In its final form, the proposed algorithm is truly concurrent in generation of prime implicants and construction of minimal forms. A convenient and efficient technique is used for identifying existing prime implicants. Branch-and-bound method is employed to restrict the search tree to a cost cut-off value depending on the definition of cost function specified. A most generalized statement of the algorithm is formulated for manual as well as computer implementation and its application is illustrated with an example. A program written in Pascal, for classical diode-gate cost function as well as PLA-area cost function, is developed and tested for an efficient computer implementation. Finally, various advantages of the proposed approach are pointed out by comparing it with the classical approach of Quine-McCluskey method.
Master of Science
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Enkosky, Thomas. "Grobner Bases and an Algorithm to Find the Monomials of an Ideal." Fogler Library, University of Maine, 2004. http://www.library.umaine.edu/theses/pdf/EnkoskyT2004.pdf.

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Wood, Peter John, and drwoood@gmail com. "Wavelets and C*-algebras." Flinders University. Informatics and Engineering, 2003. http://catalogue.flinders.edu.au./local/adt/public/adt-SFU20070619.120926.

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A wavelet is a function which is used to construct a specific type of orthonormal basis. We are interested in using C*-algebras and Hilbert C*-modules to study wavelets. A Hilbert C*-module is a generalisation of a Hilbert space for which the inner product takes its values in a C*-algebra instead of the complex numbers. We study wavelets in an arbitrary Hilbert space and construct some Hilbert C*-modules over a group C*-algebra which will be used to study the properties of wavelets. We study wavelets by constructing Hilbert C*-modules over C*-algebras generated by groups of translations. We shall examine how this construction works in both the Fourier and non-Fourier domains. We also make use of Hilbert C*-modules over the space of essentially bounded functions on tori. We shall use the Hilbert C*-modules mentioned above to study wavelet and scaling filters, the fast wavelet transform, and the cascade algorithm. We shall furthermore use Hilbert C*-modules over matrix C*-algebras to study multiwavelets.
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Hansen, Nils Bahne [Verfasser]. "Structure Analysis of the Pohlmeyer-Rehren Lie Algebra and Adaptations of the Hall Algorithm to Non-Free Graded Lie Algebras / Nils Bahne Hansen." Göttingen : Niedersächsische Staats- und Universitätsbibliothek Göttingen, 2021. http://d-nb.info/1236401646/34.

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Linfoot, Andy James. "A Case Study of A Multithreaded Buchberger Normal Form Algorithm." Diss., The University of Arizona, 2006. http://hdl.handle.net/10150/305141.

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Groebner bases have many applications in mathematics, science, and engineering. This dissertation deals with the algorithmic aspects of computing these bases. The dissertation begins with a brief introduction of fundamental concepts about Groebner bases. Following this a discussion of various implementation issues are discussed. Much of the practical difficulties of using Groebner basis algorithms and techniques stems from the high computational complexity. It is shown that the algorithmic complexity of computing a Groebner basis primarily stems from the calculation of normal forms. This is established by studying run profiles of various computations. This leads to two options of making Groebner basis techniques more practical. They are to reduce the complexity by developing new algorithms (heuristics) or reduce running time of normal form calculations by introducing concurrency. The later approach is taken in the remainder of the dissertation where a multithreaded normal form algorithm is presented and discussed. It is shown with a simple example that the new algorithm demonstrates a speedup and scalability. The algorithm also has the advantage of being completion strategy independent. We conclude with an outline of future research involving the new algorithm.
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Neverauskas, Aurimas. "Lygčių ir nelygybių simbolinio sprendimo lygiagretusis metodas." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2011. http://vddb.laba.lt/obj/LT-eLABa-0001:E.02~2011~D_20110831_140404-69461.

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Pateiktas lygčių ir nelygybių simbolinio sprendimo lygiagretus algoritmas ir jo analizė, palyginimas su neefektyvia algoritmo realizacija. Atliktas įgyvendinto algoritmo tyrimas, nustatant jo spartos priklausomybes nuo aplinkos ir užduoties, palyginant rezultatus su esama PĮ. Taip pat, šiame darbe aptariami sukurtos programų sistemos architektūriniai sprendimai: MVC patern‘as (design pattern), „Svogūno“ architektūra, priklausomybių injekcijos (Dependency Injections). Šie architektūriniai sprendimai yra pranašesni už standartinę sluoksninę architekūrą, jais paremta PĮ yra lengviau palaikoma ir modifikuojama. Šiais laikais dauguma kompiuterių turi daugiabranduolius procesorius, tačiau esama PĮ jų neišnaudoja. Šio darbo tikslas yra sukurti tokią lygčių ir nelygybių simbolinio sprendimo lygiagrečiu metodu realizaciją, kuri panaudodama turimą skaičiavimų galią, sutrumpintų skaičiavimų laiką. Atlikus tyrimus nustatyta, jog sukurtoji PĮ yra pranašesnė už Maple CAS tik tuo atveju, kai uždavinio sąlyga nėra didelė, bet reikalaujama didelės skaičiavimų galios (nelygybių sistemų sprendimas). Tačiau sprendžiant didelės apimties lygčių sistemas (40-50 nežinomųjų ir tiek pat lygčių) sukurtoji PĮ atsilieka nuo Maple CAS, kadangi daug laiko sugaištama nagrinėjant pateiktą užduotį ir skaidant ją į dalinius uždavinius.
I have presented an effective way to solve symbolic systems of equations and inequalities using parallel processes and compared it to ineffective method. Also, I have performed analysis of presented algorithm, determining its performance dependencies and comparing its performance to existing software. Also, this paper discusses architectural solutions for the application system: MVC design pattern, "Onion" architecture and Dependency Injection. These architectural patterns benefit more than standard layered architecture, software, based on these patterns, is more maintainable and changeable. These days, computers usually have multi-core processors, but not all software use them efficiently. The main problem is to create algorithm for solving symbolic systems of equations and inequalities using parallel processes, using calculation power and decreasing calculation time. Such application system was created and analyzed in this paper. It was determined that created software is superior to Maple CAS when task is small by input but requires a lot of calculating power (systems of inequalities). On the other hand, results differ when task consist of plenty of equations (40-50 equations in system, same number of unknowns). Created software falls behind Maple CAS in performance. The main reason, for this, is that created software spends too much time to analyze task and strings in it.
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Books on the topic "Algorithm algebra"

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Bultheel, Adhemar. Linear algebra, rational approximation, and orthogonal polynomials. Amsterdam: Elsevier, 1997.

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1951-, Cohen G., Giusti Marc, and Mora Teo, eds. Applied algebra, algebraic algorithms, and error-correcting codes: 11th international symposium, AAECC-11, Paris, France, July 1995 : proceedings. Berlin: Springer-Verlag, 1995.

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Davenport, James Harold. Computer algebra: Systems and algorithms for algebraic computation. 2nd ed. London: Academic Press, 1993.

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Davenport, J. H. Computer algebra: Systems and algorithms for algebraic computation. London: Academic, 1988.

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Y, Siret, and Tournier E, eds. Computer algebra: Systems and algorithms for algebraic computation. London: Academic Press, 1988.

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Sakata, Shojiro, ed. Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/3-540-54195-0.

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Mattson, Harold F., Teo Mora, and T. R. N. Rao, eds. Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/3-540-54522-0.

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Cohen, Gérard, Teo Mora, and Oscar Moreno, eds. Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. Berlin, Heidelberg: Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/3-540-56686-4.

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Boztaş, Serdar, and Igor E. Shparlinski, eds. Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/3-540-45624-4.

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Huguet, Llorenç, and Alain Poli, eds. Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/3-540-51082-6.

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Book chapters on the topic "Algorithm algebra"

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Gelfand, Israel M., and Alexander Shen. "The division algorithm." In Algebra, 6–7. Boston, MA: Birkhäuser Boston, 2004. http://dx.doi.org/10.1007/978-1-4612-0335-3_6.

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Gelfand, Israel M., and Alexander Shen. "The multiplication table and the multiplication algorithm." In Algebra, 5–6. Boston, MA: Birkhäuser Boston, 2004. http://dx.doi.org/10.1007/978-1-4612-0335-3_5.

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Childs, Lindsay N. "Euclid’s Algorithm." In A Concrete Introduction to Higher Algebra, 25–46. New York, NY: Springer New York, 1995. http://dx.doi.org/10.1007/978-1-4419-8702-0_3.

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Camion, P. "An Iterative Euclidean Algorithm." In Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, 88–128. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/3-540-51082-6_72.

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Geddes, K. O., S. R. Czapor, and G. Labahn. "The Risch Integration Algorithm." In Algorithms for Computer Algebra, 511–73. Boston, MA: Springer US, 1992. http://dx.doi.org/10.1007/978-0-585-33247-5_12.

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Nagasaka, Kosaku, and Takaaki Masui. "Extended QRGCD Algorithm." In Computer Algebra in Scientific Computing, 257–72. Cham: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-02297-0_22.

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Canny, J. F. "An improved sign determination algorithm." In Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, 108–17. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/3-540-54522-0_100.

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Conti, Pasqualina, and Carlo Traverso. "Buchberger algorithm and integer programming." In Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, 130–39. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/3-540-54522-0_102.

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Norton, Graham. "A shift-remainder GCD algorithm." In Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, 350–56. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/3-540-51082-6_91.

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Caboara, Massimo, Pasqualina Conti, and Carlo Traverse. "Yet another ideal decomposition algorithm." In Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, 39–54. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/3-540-63163-1_4.

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Conference papers on the topic "Algorithm algebra"

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Zhihua, Hu, and Liao Xiaoyong. "SMS4 Algorithm Algebra Fault Attack." In 2010 Third International Symposiums on Electronic Commerce and Security (ISECS). IEEE, 2010. http://dx.doi.org/10.1109/isecs.2010.34.

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Belisle, Cathryn M., and Pamela A. Horner. "Image algebra algorithm development environment." In San Diego '92, edited by Paul D. Gader, Edward R. Dougherty, and Jean C. Serra. SPIE, 1992. http://dx.doi.org/10.1117/12.60639.

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Wu, Dimin, and Zhengzhi Wang. "Strapdown inertial navigation algorithm in geometric algebra." In 2011 International Conference on Electrical and Control Engineering (ICECE). IEEE, 2011. http://dx.doi.org/10.1109/iceceng.2011.6058074.

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Duchateau, A. X., D. Padua, and D. Barthou. "Hydra: Automatic algorithm exploration from linear algebra equations." In 2013 IEEE/ACM International Symposium on Code Generation and Optimization (CGO). IEEE, 2013. http://dx.doi.org/10.1109/cgo.2013.6494999.

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Ammu, S., and A. S. Remya Ajai. "VLSI implementation of Boolean algebra based cryptographic algorithm." In 2016 International Conference on Electrical, Electronics, and Optimization Techniques (ICEEOT). IEEE, 2016. http://dx.doi.org/10.1109/iceeot.2016.7755059.

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de Sousa, Celso Andre Rodrigues. "Analysis of the backpropagation algorithm using linear algebra." In 2012 International Joint Conference on Neural Networks (IJCNN 2012 - Brisbane). IEEE, 2012. http://dx.doi.org/10.1109/ijcnn.2012.6252364.

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Shang, Jielin, Qiong Qin, and Hongmei Pei. "Application of Intelligent Algorithm in Linear Algebra Teaching." In 2021 2nd International Conference on Information Science and Education (ICISE-IE). IEEE, 2021. http://dx.doi.org/10.1109/icise-ie53922.2021.00101.

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Eriksson, Leif, and Victor Lagerkvist. "Improved Algorithms for Allen's Interval Algebra: a Dynamic Programming Approach." In Thirtieth International Joint Conference on Artificial Intelligence {IJCAI-21}. California: International Joint Conferences on Artificial Intelligence Organization, 2021. http://dx.doi.org/10.24963/ijcai.2021/258.

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Abstract:
The constraint satisfaction problem (CSP) is an important framework in artificial intelligence used to model e.g. qualitative reasoning problems such as Allen's interval algebra A. There is strong practical incitement to solve CSPs as efficiently as possible, and the classical complexity of temporal CSPs, including A, is well understood. However, the situation is more dire with respect to running time bounds of the form O(f(n)) (where n is the number of variables) where existing results gives a best theoretical upper bound 2^O(n * log n) which leaves a significant gap to the best (conditional) lower bound 2^o(n). In this paper we narrow this gap by presenting two novel algorithms for temporal CSPs based on dynamic programming. The first algorithm solves temporal CSPs limited to constraints of arity three in O(3^n) time, and we use this algorithm to solve A in O((1.5922n)^n) time. The second algorithm tackles A directly and solves it in O((1.0615n)^n), implying a remarkable improvement over existing methods since no previously published algorithm belongs to O((cn)^n) for any c. We also extend the latter algorithm to higher dimensions box algebras where we obtain the first explicit upper bound.
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Kumar, N., P. Gupta, M. Sahu, and M. A. Rizvi. "Boolean Algebra based effective and efficient asymmetric key cryptography algorithm: BAC algorithm." In 2013 International Multi-Conference on Automation, Computing, Communication, Control and Compressed Sensing (iMac4s). IEEE, 2013. http://dx.doi.org/10.1109/imac4s.2013.6526417.

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Kandemir, Mahmut. "A dynamic locality optimization algorithm for linear algebra codes." In the 2001 ACM symposium. New York, New York, USA: ACM Press, 2001. http://dx.doi.org/10.1145/372202.372788.

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Reports on the topic "Algorithm algebra"

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Chang, P. A Differential Algebraic Integration Algorithm for Symplectic Mappings in Systems with Three-Dimensional Magnetic Field. Office of Scientific and Technical Information (OSTI), September 2004. http://dx.doi.org/10.2172/833057.

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Bennett, Janine Camille, David Minot Day, and Scott A. Mitchell. Summary of the CSRI Workshop on Combinatorial Algebraic Topology (CAT): Software, Applications, & Algorithms. Office of Scientific and Technical Information (OSTI), November 2009. http://dx.doi.org/10.2172/1324989.

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Martín, A., L. Cirrottola, A. Froehly, R. Rossi, and C. Soriano. D2.2 First release of the octree mesh-generation capabilities and of the parallel mesh adaptation kernel. Scipedia, 2021. http://dx.doi.org/10.23967/exaqute.2021.2.010.

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This document presents a description of the octree mesh-generation capabilities and of the parallel mesh adaptation kernel. As it is discussed in Section 1.3.2 of part B of the project proposal there are two parallel research lines aimed at developing scalable adaptive mesh refinement (AMR) algorithms and implementations. The first one is based on using octree-based mesh generation and adaptation for the whole simulation in combination with unfitted finite element methods (FEMs) and the use of algebraic constraints to deal with non-conformity of spaces. On the other hand the second strategy is based on the use of an initial octree mesh that, after make it conforming through the addition of templatebased tetrahedral refinements, is adapted anisotropically during the calculation. Regarding the first strategy the following items are included:
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