Relevant bibliographies by topics / Algebraic functions – Computer programs

Contents

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

Academic literature on the topic 'Algebraic functions – Computer programs'

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Published: 4 June 2021
Last updated: 16 February 2022

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Journal articles on the topic "Algebraic functions – Computer programs"

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JACKSON, MARCEL, and TIM STOKES. "MODAL RESTRICTION SEMIGROUPS: TOWARDS AN ALGEBRA OF FUNCTIONS." International Journal of Algebra and Computation 21, no. 07 (November 2011): 1053–95. http://dx.doi.org/10.1142/s0218196711006844.

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Restriction semigroups model algebras of partial maps under composition and domain. Here we consider restriction semigroups for which the usual Boolean operations on domains are modeled. Such algebras are capable of modeling the usual modal operators considered in dynamic logic. Indeed adding a natural functional variant of union to the signature gives a deterministic version of the modal semirings of Möller and Struth, but also a monoidal version of the classical restriction categories of Cockett and Manes. Other operations modeled are intersection and (in the finite case) functional iteration. In each case, axiomatizations of the concrete functional examples are given, leading to algebraic models of partial maps incorporating all the domain-related and set-theoretic operations previously considered. Our algebras furnish natural algebraic semantics for the logics of deterministic computer programs, leading to new results for some variants of propositional dynamic logic.
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Zapatera, Alberto, and Eduardo Quevedo. "The Initial Algebraic Knowledge of Preservice Teachers." Mathematics 9, no. 17 (September 1, 2021): 2117. http://dx.doi.org/10.3390/math9172117.

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Early algebra proposes to incorporate algebra in primary school from the first years of schooling. The success of this incorporation depends, to a large extent, on the training of teachers, so the objective of this article is to study whether the degree of algebraic knowledge of student teachers at the beginning of their training. To conduct this, 106 preservice teachers were given a questionnaire. This survey is based on two daily life situations. They had to propose tasks to develop algebraic reasoning in primary school students. Most of the participants designed tasks in which they assigned specific values to the indeterminate ones and solved them arithmetically. In this way, they transformed open situations and numerous opportunities to promote algebraic thinking in students through the generalization and representation of relationships and functions into closed single-solution problems that do not promote algebraic thinking. We can see from the results that the participants’ algebraic knowledge is insufficient. Therefore, it is necessary to include in their training process the programs and experiences that will allow them to design tasks in order to detect and promote algebraic thinking in their future students. Sequences of tasks are presented to develop both situations by generalizing and representing relationships and functions, which can serve as a starting point for future training programs and experiences.
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Soo, Khí-Uí, and Tim Stokes. "Algebraic properties of if-then-else and commutative three-valued tests." International Journal of Algebra and Computation 29, no. 04 (June 2019): 743–59. http://dx.doi.org/10.1142/s0218196719500255.

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This paper establishes a finite axiomatization of possibly non-halting computer programs and tests, with the if-then-else operation. The model is a two-sorted algebra, with one sort being the programs and the other being the tests. The main operation on programs is composition, and 1 and 0 represent the programs skip and loop (i.e. never halts) respectively. Programs are modeled as partial functions on some state space [Formula: see text], with tests modeled as partial predicates on [Formula: see text]. The operations on the tests are the usual logical connectives ∧, ∨, [Formula: see text], [Formula: see text] and [Formula: see text]. In addition, there is the hybrid operation of if-then-else, and the test-valued operation [Formula: see text] on programs which is true when a program halts, and undefined otherwise. The halting operation [Formula: see text] implies that operations of domain [Formula: see text] and domain join ∨ may also be expressed. When tests are assumed to be possibly non-halting, the evaluation strategy of the logical connectives affects the result. Here we model parallel evaluation, as opposed to the common sequential (or short-circuit) evaluation strategy. For example, we view [Formula: see text] as false if either [Formula: see text] or [Formula: see text] is false, even if the other does not halt.
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Choporov, S. V., M. S. Ihnatchenko, O. V. Kudin, A. G. Kryvokhata, and S. I. Homeniuk. "IMPLEMENTATION OF A FINITE ELEMENT CLASS LIBRARY USING GENERALIZED PROGRAMMING." Radio Electronics, Computer Science, Control, no. 2 (July 10, 2021): 164–73. http://dx.doi.org/10.15588/1607-3274-2021-2-17.

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Context. For computer modeling of complex objects and phenomena of various nature, in practice, the numerical finite element method is often used. Its software implementation (especially for the study of new classes of problems) is a rather laborious process. The high cost of software development makes the development of new approaches to improving the efficiency of programming and maintenance (including the addition of new functions) urgent. Objective. The aim of the work is to create a new effective architecture of programs for finite element analysis of problems in mathematical physics, which makes it easy to expand their functionality to solve new classes of problems. Method. A method for developing programs for finite element analysis using generalized programming is proposed, which makes it possible to significantly simplify the architecture of the software and make it more convenient for maintenance and modification by separating algorithms and data structures. A new architecture of classes that implement finite element calculation is proposed, which makes it possible to easily expand the functionality of programs by adding new types of finite elements, methods for solving systems of linear algebraic equations, parallel computations, etc. Results. The proposed approach was implemented in software as a class library in C ++. A number of computational experiments have been carried out, which have confirmed its efficiency in solving practical problems. Conclusions. The developed approach can be used both to create general-purpose finite element analysis systems with an open architecture, and to implement specialized software packages focused on solving specific classes of problems (fracture mechanics, elastomers, contact interaction, etc.).
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Biela, Andrzej. "Retrieval System and Dynamic Algorithm Looking for Axioms of Notions Defined by Programs." Fundamenta Informaticae 19, no. 3-4 (October 1, 1993): 275–301. http://dx.doi.org/10.3233/fi-1993-193-404.

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In this paper we shall introduce a formal system of algorithmic logic which enables us to formulate some problems connected with a retrieval system which provides a comprehensive tool in automated theorem proving of theorems consisting of programs, procedures and functions. The procedures and functions may occur in considered theorems while the program of the above mentioned system is being executed. We can get an answer whether some relations defined by programs hold and we can prove functional equations in a dynamic way by looking for a special set of axioms /assumptions/ during the execution of system. We formulate RS-algorithm which enables us to construct the set of axioms for proving some properties of functions and relations defined by programs. By RS-algorithm we get the dynamic process of proving functional equations and we can answer the question whether some relations defined by programs hold. It enables us to solve some problems concerning the correctness of programs. This system can be used for giving an expert appraisement. We shall provide the major structures and a sketch of an implementation of the above formal system.
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Albert, Elvira, Nikolaos Bezirgiannis, Frank de Boer, and Enrique Martin-Martin. "A Formal, Resource Consumption-Preserving Translation from Actors with Cooperative Scheduling to Haskell*." Fundamenta Informaticae 177, no. 3-4 (December 10, 2020): 203–34. http://dx.doi.org/10.3233/fi-2020-1988.

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We present a formal translation of a resource-aware extension of the Abstract Behavioral Specification (ABS) language to the functional language Haskell. ABS is an actor-based language tailored to the modeling of distributed systems. It combines asynchronous method calls with a suspend and resume mode of execution of the method invocations. To cater for the resulting cooperative scheduling of the method invocations of an actor, the translation exploits for the compilation of ABS methods Haskell functions with continuations. The main result of this article is a correctness proof of the translation by means of a simulation relation between a formal semantics of the source language and a high-level operational semantics of the target language, i.e., a subset of Haskell. We further prove that the resource consumption of an ABS program extended with a cost model is preserved over this translation, as we establish an equivalence of the cost of executing the ABS program and its corresponding Haskell-translation. Concretely, the resources consumed by the original ABS program and those consumed by the Haskell program are the same, considering a cost model. Consequently, the resource bounds automatically inferred for ABS programs extended with a cost model, using resource analysis tools, are sound resource bounds also for the translated Haskell programs. Our experimental evaluation confirms the resource preservation over a set of benchmarks featuring different asymptotic costs.
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Blikle, Andrzej. "Three-Valued Predicates for Software Specification and Validation." Fundamenta Informaticae 14, no. 4 (April 1, 1991): 387–410. http://dx.doi.org/10.3233/fi-1991-14402.

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Partial functions, hence also partial predicates, cannot be avoided in algorithms. However, in spite of the fact that partial functions have been formally introduced into the theory of software very early, partial predicates are still not quite commonly recognized. In many programming- and software-specification languages partial Boolean expressions are treated in a rather simplistic way: the evaluation of a Boolean sub-expression to an error leads to the evaluation of the hosting Boolean expression to an error and, in the consequence, to the abortion of the whole program. This technique is known as an eager evaluation of expressions. A more practical approach to the evaluation of expressions – gaining more interest today among both theoreticians and programming-language designers – is lazy evaluation. Lazily evaluated Boolean expressions correspond to (non-strict) three-valued predicates where the third value represents both an error and an undefinedness. On the semantic ground this leads to a three-valued propositional calculus, three-valued quantifiers and an appropriate logic. This paper is a survey-essay devoted to the discussion and the comparison of a few three-valued propositional and predicate calculi and to the discussion of the author’s claim that a two-valued logic, rather than a three-valued logic, is suitable for the treatment of programs with three-valued Boolean expressions. The paper is written in a formal but not in a formalized style. All discussion is carried on a semantic ground. We talk about predicates (functions) and a semantic consequence relation rather than about expressions and inference rules. However, the paper is followed by more formalized works which carry our discussion further on a formalized ground, and where corresponding formal logics are constructed and discussed.
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Adel'shin, I. M., and M. I. Vodinchar. "Algebraic representation of structured R-programs." Cybernetics 24, no. 5 (September 1988): 555–64. http://dx.doi.org/10.1007/bf01255667.

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Platzer, A. "Differential-algebraic Dynamic Logic for Differential-algebraic Programs." Journal of Logic and Computation 20, no. 1 (November 18, 2008): 309–52. http://dx.doi.org/10.1093/logcom/exn070.

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Brisebarre, Nicolas, and Jean-Michel Muller. "Correct rounding of algebraic functions." RAIRO - Theoretical Informatics and Applications 41, no. 1 (January 2007): 71–83. http://dx.doi.org/10.1051/ita:2007002.

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Dissertations / Theses on the topic "Algebraic functions – Computer programs"

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Schanzer, Emmanuel Tanenbaum. "Algebraic Functions, Computer Programming, and the Challenge of Transfer." Thesis, Harvard University, 2015. http://nrs.harvard.edu/urn-3:HUL.InstRepos:16461037.

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Students' struggles with algebra are well documented. Prior to the introduction of functions, mathematics is typically focused on applying a set of arithmetic operations to compute an answer. The introduction of functions, however, marks the point at which mathematics begins to focus on building up abstractions as a way to solve complex problems. A common refrain about word problems is that “the equations are easy to solve - the hard part is setting them up!” A student of algebra is asked to identify functional relationships in the world around them - to set up the equations that describe a system- and to reason about these relationships. Functions, in essence, mark the shift from computing answers to solving problems. Researchers have called for this shift to accompany a change in pedagogy, and have looked to computer programming and game design as a means to combine mathematical rigor with creative inquiry. Many studies have explored the impact of teaching students to program, with the goal of having them transfer what they have learned back into traditional mathematics. While some of these studies have shown positive outcomes for concepts like geometry and fractions, transfer between programming and algebra has remained elusive. The literature identifies a number of conditions that must be met to facilitate transfer, including careful attention to content, software, and pedagogy. This dissertation is a feasibility study of Bootstrap, a curricular intervention based on best practices from the transfer and math-education literature. Bootstrap teaches students to build a video game by applying algebraic concepts and a problem solving technique in the programming domain, with the goal of transferring what they learn back into traditional algebra tasks. The study employed a mixed-methods analysis of six Bootstrap classes taught by math and computer science teachers, pairing pre- and post-tests with classroom observations and teacher interviews. Despite the use of a CS-derived problem solving technique, a programming language and a series of programming challenges, students were able to transfer what they learned into traditional algebra tasks and math teachers were found to be more successful at facilitating this transfer than their CS counterparts.
Education Policy, Leadership, and Instructional Practice
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Klingler, Carol Diane. "Syntax-directed semantics-supported editing of algebraic specifications." Master's thesis, This resource online, 1990. http://scholar.lib.vt.edu/theses/available/etd-01202010-020048/.

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Müller-Olm, Markus. "Modular compiler verification : a refinement algebraic approach advocating stepwise abstraction /." Berlin [u.a.] : Springer, 1997. http://www.loc.gov/catdir/enhancements/fy0815/97013428-d.html.

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Forbes, Michael Andrew. "Polynomial identity testing of read-once oblivious algebraic branching programs." Thesis, Massachusetts Institute of Technology, 2014. http://hdl.handle.net/1721.1/89843.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2014.
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Cataloged from student-submitted PDF version of thesis.
Includes bibliographical references (pages 209-220).
We study the problem of obtaining efficient, deterministic, black-box polynomial identity testing algorithms (PIT) for algebraic branching programs (ABPs) that are read-once and oblivious. This class has an efficient, deterministic, white-box polynomial identity testing algorithm (due to Raz and Shpilka [RS05]), but prior to this work there was no known such black-box algorithm. The main result of this work gives the first quasi-polynomial sized hitting set for size S circuits from this class, when the order of the variables is known. As our hitting set is of size exp(lg2 S), this is analogous (in the terminology of boolean pseudorandomness) to a seed-length of lg2 S, which is the seed length of the pseudorandom generators of Nisan [Nis92] and Impagliazzo-Nisan-Wigderson [INW94] for read-once oblivious boolean branching programs. Thus our work can be seen as an algebraic analogue of these foundational results in boolean pseudorandomness. We also show that several other circuit classes can be black-box reduced to readonce oblivious ABPs, including non-commutative ABPs and diagonal depth-4 circuits, and consequently obtain similar hitting sets for these classes as well. To establish the above hitting sets, we use a form of dimension reduction we call a rank condenser, which maps a large-dimensional space to a medium-dimensional space, while preserving the rank of low-dimensional subspaces. We give an explicit construction of a rank condenser that is randomness efficient and show how it can be used as a form of oblivious Gaussian elimination. As an application, we strengthen a result of Mulmuley [Mul12a], and show that derandomizing a particular case of the Noether Normalization Lemma is reducible to black-box PIT of read-once oblivious ABPs. Using our hitting set results, this gives a derandomization of Noether Normalization in that case.
by Michael Andrew Forbes.
Ph. D.
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McCay, Matthew Eric. "Computing the Algebraic Immunity of Boolean Functions on the SRC-6 Reconfigurable Computer." Thesis, Monterey, California. Naval Postgraduate School, 2012. http://hdl.handle.net/10945/6831.

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Boolean functions with high algebraic immunity (AI) are vital in reducing the possibility of utilizing algebraic attacks to break an encryption system. Simple algorithms exist to compute the AI of a given n-variable Boolean function, but the time required to test a large number of functions is much greater on conventional computing systems. AI was computed for all functions through n = 5 using the SRC-6. AI was also computed for n = 5 using a C algorithm. The SRC-6 performed 4.86 times faster than a conventional processor for this computation. It is believed that this is the first enumeration of all 5-variable functions with respect to AI. Monte Carlo trials were performed for n = 6, both on the SRC-6 and utilizing a C algorithm on a conventional processor. These trials provided the first known distribution of AI for 6-variable functions. Some algorithms for computing AI require a conversion between the truth table form of the function and its algebraic normal form. The first known Verilog implementation of a reduced transeunt triangle was developed for this conversion. This reduced form requires many fewer gates and has (n) delay versus (2) n delay for a full transeunt triangle.
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Song, Ning. "Minimization of Exclusive Sum of Products Expressions for Multiple-Valued Input Incompletely Specified Functions." PDXScholar, 1992. https://pdxscholar.library.pdx.edu/open_access_etds/4684.

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In recent years, there is an increased interest in the design of logic circuits which use EXOR gates. Particular interest is in the minimization of arbitrary Exclusive Sums Of Products (ESOPs). Functions realized by such circuits can have fewer gates, fewer connections, and take up less area in VLSI and especially, FPGA realizations. They are also easily testable. So far, the ESOPs are not as popular as their Sum of Products (SOP) counterparts. One of the main reasons it that the problem of the minimization of ESOP circuits was traditionally an extremely difficult one. Since exact solutions can be practically found only for functions with not more than 5 variables the interest is in approximate solutions. Two approaches to generate s~b optimal solutions can be found in the literature. One approach is to minimize sub-families of ESOPs. Another approach is to minimize ESOPs using heuristic algorithms. The method we introduced in this thesis belongs to the second approach, which normally generates better results than the first approach. In the second approach, two general methods are used. One method is to minimize the coefficients of Reed-Muller forms. Another method is to perform a set of cube operations iteratively on a given ESOP. So far, this method has achieved better results than other methods. In this method (we call it cube operation approach), the quality of the results depends on the quality of the cube operations. Different cube operations have been invented in the past a few years. All these cube operations can be applied only when some conditions are satisfied. This is due to the limitations of the operations. These limitations reduce the opportunity to get a high quality solution and reduce the efficiency of the algorithm as well. The efforts of removing these limitations led to the invention of our new cube operation, exorlink, which is introduced in this thesis. Exorlink can be applied on any two cubes in the array without condition. All the existing cube operations in this approach are included in it. So this is the most general operation in this approach. Another key issue in the cube operation approach is the efficiency of the algorithm. Existing algorithms perform all possible cube operations, and give litter guide to select the operations. Our new algorithm selectively performs some of the possible operations. Experimental results show that this algorithm is more efficient than existing ones. New algorithms to minimize multiple output functions and especially incompletely specified ESOPs are also presented. The algorithms are included in the program EXORCISM-MV -2, which is a new version of EXORCISM-MY. EXORCISM-MV -2 was tested on many benchmark functions and compared to the results from literature. The program in most cases gives the same or better solutions on binary and 4-valued completely specified functions. More importantly, it is able to efficiently minimize arbitrary-valued and incompletely specified functions, while the programs from literature are either for completely specified functions, or for binary variables. Additionally, as in Espresso, the number of variables in our program is unlimited and the only constraint is the number of input cubes that are read, so very large functions can be minimized. Based on our new cube operation and new algorithms, in the thesis, we present a solution to a problem that has not yet been practically solved in the literature: efficient minimization of arbitrary ESOP expressions for multiple-output multiple-valued input incompletely specified functions.
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Dhillon, Adam. "A Complexity of Real Functions based on Analog Computing." Scholarship @ Claremont, 2019. https://scholarship.claremont.edu/hmc_theses/225.

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This thesis is focused on analyzing a particular notion of complexity of real valued functions through the lens of analog computers. This report features design changes to Pour-El’s notion of an analog computer that reflect this question of complexity in a concrete way. Additionally, these changes to the analog computer allow an extension of Pour-El’s work in which the complexity of a function can be identified with the order of a differentiably algebraic equation that the function satisfies.
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Maddock, Thomas III, and Laurel J. Lacher. "MODRSP: a program to calculate drawdown, velocity, storage and capture response functions for multi-aquifer systems." Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1991. http://hdl.handle.net/10150/620142.

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MODRSP is program used for calculating drawdown, velocity, storage losses and capture response functions for multi - aquifer ground -water flow systems. Capture is defined as the sum of the increase in aquifer recharge and decrease in aquifer discharge as a result of an applied stress from pumping [Bredehoeft et al., 19821. The capture phenomena treated by MODRSP are stream- aquifer leakance, reduction of evapotranspiration losses, leakance from adjacent aquifers, flows to and from prescribed head boundaries and increases or decreases in natural recharge or discharge from head dependent boundaries. The response functions are independent of the magnitude of the stresses and are dependent on the type of partial differential equation, the boundary and initial conditions and the parameters thereof, and the spatial and temporal location of stresses. The aquifers modeled may have irregular -shaped areal boundaries and non -homogeneous transmissive and storage qualities. For regional aquifers, the stresses are generally pumpages from wells. The utility of response functions arises from their capacity to be embedded in management models. The management models consist of a mathematical expression of a criterion to measure preference, and sets of constraints which act to limit the preferred actions. The response functions are incorporated into constraints that couple the hydrologic system with the management system (Maddock, 1972). MODRSP is a modification of MODFLOW (McDonald and Harbaugh, 1984,1988). MODRSP uses many of the data input structures of MODFLOW, but there are major differences between the two programs. The differences are discussed in Chapters 4 and 5. An abbreviated theoretical development is presented in Chapter 2, a more complete theoretical development may be found in Maddock and Lacher (1991). The finite difference technique discussion presented in Chapter 3 is a synopsis of that covered more completely in McDonald and Harbaugh (1988). Subprogram organization is presented in Chapter 4 with the data requirements explained in Chapter 5. Chapter 6 contains three example applications of MODRSP.
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Haug, Mark. "Nonparametric density estimation for univariate and bivariate distributions with applications in discriminant analysis for the bivariate case." Thesis, Kansas State University, 1986. http://hdl.handle.net/2097/9916.

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Kim, Jongwoo. "A robust hough transform based on validity /." free to MU campus, to others for purchase, 1997. http://wwwlib.umi.com/cr/mo/fullcit?p9842545.

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Books on the topic "Algebraic functions – Computer programs"

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Boolean functions: With engineering applications and computer programs. Berlin: Springer-Verlag, 1989.

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Schneeweiss, Winfrid G. Boolean Functions: With Engineering Applications and Computer Programs. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989.

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Timochouk, Leonid A. Constructive algebraic methods for some problems in non-linear analysis: Doctor thesis. [York?]: L.A. Timochouk, 1997.

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Porwik, Piotr. Widmowe modelowanie systemów cyfrowych o zadanych cechach. Katowice: Wydawn. Uniwersytetu Śląskiego, 2000.

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Heinrich, Hussmann. Nondeterminism in algebraic specifications and algebraic programs. Boston: Birkhäuser, 1993.

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Rattray, Charles. Algebraic specification for practical software production. London: Kogan Page, 1988.

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Jonasson, Jesper. Reuse of algebraic specifications. Dublin: University College Dublin, 1995.

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Methods and programs for mathematical functions. Chichester, England: E. Horwood, 1989.

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Glover, Daniel. Subband/transform functions for image processing. [Washington, DC]: National Aeronautics and Space Administration, 1993.

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Dinwiddie, Robert. Excel: Formulas & functions. New York, NY: DK Publishing, 2002.

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Book chapters on the topic "Algebraic functions – Computer programs"

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Berghammer, Rudolf, and Sebastian Fischer. "Simple Rectangle-Based Functional Programs for Computing Reflexive-Transitive Closures." In Relational and Algebraic Methods in Computer Science, 114–29. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-33314-9_8.

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Kozen, Dexter, Susan Landau, and Richard Zippel. "Decomposition of algebraic functions." In Lecture Notes in Computer Science, 80–92. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/3-540-58691-1_46.

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Doroshenko, Anatoly E., and Alexander B. Godlevsky. "Parallelising programs with algebraic programming tools." In Lecture Notes in Computer Science, 685–90. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/bfb0020502.

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Wu, Chuan-Kun, and Dengguo Feng. "Algebraic Immunity of Boolean Functions." In Advances in Computer Science and Technology, 147–75. Berlin, Heidelberg: Springer Berlin Heidelberg, 2016. http://dx.doi.org/10.1007/978-3-662-48865-2_5.

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Schneeweiss, Winfrid G. "Some Algorithms and Computer Programs for Boolean Analysis." In Boolean Functions, 182–217. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-642-45638-1_10.

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Kryukov, A. P., and A. Ya Rodionov. "CTS — Algebraic debugging system for reduce programs." In Lecture Notes in Computer Science, 233–43. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/3-540-51517-8_121.

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Mili, Ali, Marcelo F. Frias, and Ali Jaoua. "On Faults and Faulty Programs." In Relational and Algebraic Methods in Computer Science, 191–207. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-06251-8_12.

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Darulova, Eva, and Anastasia Volkova. "Sound Approximation of Programs with Elementary Functions." In Computer Aided Verification, 174–83. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-25543-5_11.

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Krogmeier, Paul, Umang Mathur, Adithya Murali, P. Madhusudan, and Mahesh Viswanathan. "Decidable Synthesis of Programs with Uninterpreted Functions." In Computer Aided Verification, 634–57. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-53291-8_32.

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Berghammer, Rudolf, Peter Höfner, and Insa Stucke. "Automated Verification of Relational While-Programs." In Relational and Algebraic Methods in Computer Science, 173–90. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-06251-8_11.

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Conference papers on the topic "Algebraic functions – Computer programs"

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Djalal, Boris. "A constructive formalisation of Semi-algebraic sets and functions." In CPP '18: Certified Proofs and Programs. New York, NY, USA: ACM, 2018. http://dx.doi.org/10.1145/3167099.

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Ar, S., R. J. Lipton, R. Rubinfeld, and M. Sudan. "Reconstructing algebraic functions from mixed data." In Proceedings., 33rd Annual Symposium on Foundations of Computer Science. IEEE, 1992. http://dx.doi.org/10.1109/sfcs.1992.267801.

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Slagel, J. Tanner, Lauren White, and Aaron Dutle. "Formal verification of semi-algebraic sets and real analytic functions." In CPP '21: 10th ACM SIGPLAN International Conference on Certified Programs and Proofs. New York, NY, USA: ACM, 2021. http://dx.doi.org/10.1145/3437992.3439933.

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Sharma, Naveen, and Paul S. Wang. "The PIER Parallel FEA Program Generator." In ASME 1993 International Computers in Engineering Conference and Exposition. American Society of Mechanical Engineers, 1993. http://dx.doi.org/10.1115/cie1993-0036.

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Abstract In this paper we describe a coupled symbolic-numeric approach for solving PDE-based mathematical models on sequential and parallel computers. PIER, an experimental software system that we are developing, synthesizes F77 subroutines for finite element modeling directly from very-high level user input specifications. The system is being developed in Common Lisp and uses MAXIMA computer algebra system for symbolic mathematical computations. PIER input syntax provide high-level statements to specify finite element discretization and methods for solving systems of equations. The user composes the finite element analysis process using MAXIMA input syntax and F77 statements along with these statements. Symbolic quantities for element formulation like shape functions, element equations etc. are automatically derived. The input model characteristics, derived formulae, desired solution methods, and the target machine knowledge are then used to generate numerical code for FEA solution steps. The benefits of this approach include: 1) substantially reducing the time and effort required to solve mathematical models, 2) ability to solve models in higher-dimensions, and 3) automatic retargeting of numeric computations to multiple parallel architectures. Currently, we are applying the techniques developed in our research to the numeric solution of problems in computational liquid crystal physics and the theory of elasticity. Sequent shared-memory multiprocessor is the current target parallel computer.
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O'Leary, Paul, and Matther Harker. "An Algebraic Framework for Discrete Basis Functions in Computer Vision." In Image Processing (ICVGIP). IEEE, 2008. http://dx.doi.org/10.1109/icvgip.2008.107.

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Zhang, Zhichao, Zheng Huang, Jie Zhang, and Qiaoyan Wen. "Construction of Odd-variable Boolean Functions with Optimum Algebraic Immunity." In 2nd International Symposium on Computer, Communication, Control and Automation. Paris, France: Atlantis Press, 2013. http://dx.doi.org/10.2991/isccca.2013.21.

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Baoguo, Wang, Hua Yaonan, Huang Xiaoyan, and Wu Chung-Hua. "Transonic Flow Along Arbitrary Stream Filament of Revolution Solved by Separate Computations With Shock Fitting." In ASME 1986 International Gas Turbine Conference and Exhibit. American Society of Mechanical Engineers, 1986. http://dx.doi.org/10.1115/86-gt-30.

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The transonic flow field in a cascade of blades lying on an S1 stream surface of revolution is solved by separate computations in the supersonic and the transonic region. The characteristics method is used to solve the supersonic flow upstream of the passage shock and the direct matrix method is used to solve the transonic flow downstream of the passage shock. The transonic stream-function equation in weak conservative form was discretized with respect to general non-orthogonal curvilinear coordinates. Using the artificial density technique and a new iteration scheme between the stream function and the density, the set of algebraic equations was solved by the direct matrix method. A computer program has been developed and is applied to compute the flow field on several S1 stream surfaces of revolution for the DFVLR transonic axial compressor rotor. It is found that the thickness of the S1 stream filament and the variation of entropy along the streamlines have strong influence on calculation. The calculated result agrees with the experimental data fairly well.
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Bakoev, Valentin. "A Method for Fast Computing the Algebraic Degree of Boolean Functions." In CompSysTech '20: International Conference on Computer Systems and Technologies '20. New York, NY, USA: ACM, 2020. http://dx.doi.org/10.1145/3407982.3408005.

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Panta Pazos, Rube´n. "Finding the Minimun of the Quadratic Functional in Variational Approach in Transport Theory Problems." In 16th International Conference on Nuclear Engineering. ASMEDC, 2008. http://dx.doi.org/10.1115/icone16-48479.

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In this work it is reviewed the variational approach for some Transport Problems. Let X be a convex domain in Rn, and V a compact set. For that, it is considered the following equation: ∂ψ∂t(x,v,t)+v·∇ψ(x,v,t)+h(x,μ)ψ(x,v,t)==∫Vk(x,v,v′)ψ(x,v′,t)dv′+q(x,v,t)(1) where x represents the spatial variable in a domain D, v an element of a compact set V, Ψ is the angular flux, h(x,v) the collision frequency, k(x,v,v’) the scattering kernel function and q(x,v) the source function. It is put the attention in the construction of the quadratic functional J which appears in variational approaches for transport theory (for example, the Vladimirov functional). Some properties of this functional in a proper functional framework, in order to determine the minimum for J are considered. First, the general formulation is studied. Then an algorithm is given for minimizing the functional J for two remarkable problems: spherical harmonic method and spectral collocation method. A program associated to this algorithm is worked in a computer algebraic system, and also was depeloped a version in a high level language.
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Tsai, Ming-Hsien, Bow-Yaw Wang, and Bo-Yin Yang. "Certified Verification of Algebraic Properties on Low-Level Mathematical Constructs in Cryptographic Programs." In CCS '17: 2017 ACM SIGSAC Conference on Computer and Communications Security. New York, NY, USA: ACM, 2017. http://dx.doi.org/10.1145/3133956.3134076.

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