Download or read book Algebraic Approach to Data Processing written by Julio C. Urenda and published by Springer Nature. This book was released on 2022-10-15 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book explores a new general approach to selecting—and designing—data processing techniques. Symmetry and invariance ideas behind this algebraic approach have been successful in physics, where many new theories are formulated in symmetry terms. The book explains this approach and expands it to new application areas ranging from engineering, medicine, education to social sciences. In many cases, this approach leads to optimal techniques and optimal solutions. That the same data processing techniques help us better analyze wooden structures, lung dysfunctions, and deep learning algorithms is a good indication that these techniques can be used in many other applications as well. The book is recommended to researchers and practitioners who need to select a data processing technique—or who want to design a new technique when the existing techniques do not work. It is also recommended to students who want to learn the state-of-the-art data processing.

Download or read book Algebraic Approaches to Program Semantics written by Ernest G. Manes and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the 1930s, mathematical logicians studied the notion of "effective comput ability" using such notions as recursive functions, A-calculus, and Turing machines. The 1940s saw the construction of the first electronic computers, and the next 20 years saw the evolution of higher-level programming languages in which programs could be written in a convenient fashion independent (thanks to compilers and interpreters) of the architecture of any specific machine. The development of such languages led in turn to the general analysis of questions of syntax, structuring strings of symbols which could count as legal programs, and semantics, determining the "meaning" of a program, for example, as the function it computes in transforming input data to output results. An important approach to semantics, pioneered by Floyd, Hoare, and Wirth, is called assertion semantics: given a specification of which assertions (preconditions) on input data should guarantee that the results satisfy desired assertions (postconditions) on output data, one seeks a logical proof that the program satisfies its specification. An alternative approach, pioneered by Scott and Strachey, is called denotational semantics: it offers algebraic techniques for characterizing the denotation of (i. e. , the function computed by) a program-the properties of the program can then be checked by direct comparison of the denotation with the specification. This book is an introduction to denotational semantics. More specifically, we introduce the reader to two approaches to denotational semantics: the order semantics of Scott and Strachey and our own partially additive semantics.

Download or read book Programming Languages and Systems written by Wei-Ngan Chin and published by Springer Science & Business Media. This book was released on 2004-10-15 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the Second Asian Symposium on Programming Languages and Systems, APLAS 2004, held in Taipei, Taiwan in November 2004. The 26 revised full papers presented together with abstracts of 3 invited talks were carefully reviewed and selected from 97 submissions. Among the topics covered are type theory, program transformation, static analysis, verification, concurrent systems, code generation, programming calculi, functional programming languages, language support, component systems, real-time systems, embedded systems, formal systems design, object-oriented design, Java objects, program optimization .

Download or read book Quantum Logic in Algebraic Approach written by Miklós Rédei and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work has grown out of the lecture notes that were prepared for a series of seminars on some selected topics in quantum logic. The seminars were delivered during the first semester of the 1993/1994 academic year in the Unit for Foundations of Science of the Department of History and Foundations of Mathematics and Science, Faculty of Physics, Utrecht University, The Netherlands, while I was staying in that Unit on a European Community Research Grant, and in the Center for Philosophy of Science, University of Pittsburgh, U. S. A. , where I was staying during the 1994/1995 academic year as a Visiting Fellow on a Fulbright Research Grant, and where I also was supported by the Istvan Szechenyi Scholarship Foundation. The financial support provided by these foundations, by the Center for Philosophy of Science and by the European Community is greatly acknowledged, and I wish to thank D. Dieks, the professor of the Foundations Group in Utrecht and G. Massey, the director of the Center for Philosophy of Science in Pittsburgh for making my stay at the respective institutions possible. I also wish to thank both the members of the Foundations Group in Utrecht, especially D. Dieks, C. Lutz, F. Muller, J. Uffink and P. Vermaas and the participants in the seminars at the Center for Philosophy of Science in Pittsburgh, especially N. Belnap, J. Earman, A. Janis, J. Norton, and J.

Download or read book Algebraic Approach to Simple Quantum Systems written by Barry G. Adams and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the use of algebraic methods and sym bolic computation for simple quantum systems with applications to large order perturbation theory. It is the first book to integrate Lie algebras, algebraic perturbation theory and symbolic computation in a form suitable for students and researchers in theoretical and computational chemistry and is conveniently divided into two parts. The first part, Chapters 1 to 6, provides a pedagogical introduction to the important Lie algebras so(3), so(2,1), so(4) and so(4,2) needed for the study of simple quantum systems such as the D-dimensional hydrogen atom and harmonic oscillator. This material is suitable for advanced undergraduate and beginning graduate students. Of particular importance is the use of so(2,1) in Chapter 4 as a spectrum generating algebra for several important systems such as the non-relativistic hydrogen atom and the relativistic Klein-Gordon and Dirac equations. This approach provides an interesting and important alternative to the usual textbook approach using series solutions of differential equations.

Download or read book A Process Algebraic Approach to Software Architecture Design written by Alessandro Aldini and published by Springer Science & Business Media. This book was released on 2010-03-14 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inthe?eldofformalmethodsincomputerscience,concurrencytheoryisreceivinga constantlyincreasinginterest.Thisisespeciallytrueforprocessalgebra.Althoughit had been originally conceived as a means for reasoning about the semantics of c- current programs, process algebraic formalisms like CCS, CSP, ACP, ?-calculus, and their extensions (see, e.g., [154,119,112,22,155,181,30]) were soon used also for comprehendingfunctionaland nonfunctionalaspects of the behaviorof com- nicating concurrent systems. The scienti?c impact of process calculi and behavioral equivalences at the base of process algebra is witnessed not only by a very rich literature. It is in fact worth mentioningthe standardizationprocedurethat led to the developmentof the process algebraic language LOTOS [49], as well as the implementation of several modeling and analysis tools based on process algebra, like CWB [70] and CADP [93], some of which have been used in industrial case studies. Furthermore, process calculi and behavioral equivalencesare by now adopted in university-levelcourses to teach the foundations of concurrent programming as well as the model-driven design of concurrent, distributed, and mobile systems. Nevertheless, after 30 years since its introduction, process algebra is rarely adopted in the practice of software development. On the one hand, its technica- ties often obfuscate the way in which systems are modeled. As an example, if a process term comprises numerous occurrences of the parallel composition operator, it is hard to understand the communicationscheme among the varioussubterms. On the other hand, process algebra is perceived as being dif?cult to learn and use by practitioners, as it is not close enough to the way they think of software systems.

Download or read book Discrete time Signal Processing written by Darrell Williamson and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive and up-to-date book focuses on an algebraic approach to the analysis and design of discrete-time signal processors, including material applicable to numeric and symbolic computation programs such as MATLAB. Written with clarity, it contains the latest detailed research results.

Download or read book N ary Relations for Logical Analysis of Data and Knowledge written by Kulik, Boris and published by IGI Global. This book was released on 2017-11-30 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics has been used as a tool in logistical reasoning for centuries. Examining how specific mathematic structures can aid in data and knowledge management helps determine how to efficiently and effectively process more information in these fields. N-ary Relations for Logical Analysis of Data and Knowledge is a critical scholarly reference source that provides a detailed study of the mathematical techniques currently involved in the progression of information technology fields. Featuring relevant topics that include algebraic sets, deductive analysis, defeasible reasoning, and probabilistic modeling, this publication is ideal for academicians, students, and researchers who are interested in staying apprised of the latest research in the information technology field.

Download or read book Algebraic Approaches to Partial Differential Equations written by Xiaoping Xu and published by Springer. This book was released on 2015-05-19 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the various algebraic techniques for solving partial differential equations to yield exact solutions, techniques developed by the author in recent years and with emphasis on physical equations such as: the Maxwell equations, the Dirac equations, the KdV equation, the KP equation, the nonlinear Schrodinger equation, the Davey and Stewartson equations, the Boussinesq equations in geophysics, the Navier-Stokes equations and the boundary layer problems. In order to solve them, I have employed the grading technique, matrix differential operators, stable-range of nonlinear terms, moving frames, asymmetric assumptions, symmetry transformations, linearization techniques and special functions. The book is self-contained and requires only a minimal understanding of calculus and linear algebra, making it accessible to a broad audience in the fields of mathematics, the sciences and engineering. Readers may find the exact solutions and mathematical skills needed in their own research.

Download or read book Algebra of Communicating Processes written by Alban Ponse and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: ACP, the Algebra of Communicating Processes, is an algebraic approach to the study of concurrent processes, initiated by Jan Bergstra and Jan Will em Klop in the early eighties. These proceedings comprise the contributions to ACP94, the first workshop devoted to ACP. The work shop was held at Utrecht University, 16-17 May 1994. These proceedings are meant to provide an overview of current research in the area of ACP. They contain fifteen contributions. The first one is a classical paper on ACP by J.A. Bergstra and J.W. Klop: The Algebra of Recursively Defined Processes and the Algebra of Regular Processes, Report IW 235/83, Mathematical Centre, Amsterdam, 1983. It serves as an introduction to the remainder of the proceedings and, indeed, as a general introduction to ACP. An extended abstract of this paper is published under the same title in the ICALP' 84 proceedings. Of the re maining contributions, three were submitted by the invited speakers and the others were selected by the programme committee. As for the presentations, Jos Baeten, Rob van Glabbeek, Jan Friso Groote, and Frits Vaandrager were each invited to deliver a lecture. A paper relating to Frits Vaandrager's lecture has already been submitted for publication elsewhere and is not, therefore, included in these pro ceedings. Gabriel Ciobanu, one of our guests, gave an impression of his work in an extra lecture. Furthermore, ten presentations were given on the basis of selected papers.

Download or read book An Algebraic Approach to Compiler Design written by Augusto Sampaio and published by World Scientific. This book was released on 1997 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book investigates the design of compilers for procedural languages, based on the algebraic laws which these languages satisfy. The particular strategy adopted is to reduce an arbitrary source program to a general normal form, capable of representing an arbitrary target machine. This is achieved by a series of normal form reduction theorems which are proved algebraically from the more basic laws. The normal form and the related reduction theorems can then be instantiated to design compilers for distinct target machines. This constitutes the main novelty of the author's approach to compilation, together with the fact that the entire process is formalised within a single and uniform semantic framework of a procedural language and its algberaic laws. Furthermore, by mechanising the approach using the OBJ3 term rewriting system it is shown that a prototype compiler is developed as a byproduct of its own proof of correctness.

Download or read book Recent Trends in Algebraic Development Techniques written by Francesco Parisi-Presicce and published by Springer. This book was released on 1998-03-11 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the strictly refereed post-workshop proceedings of the 12th International Workshop on Algebraic Development Techniques, WADT '98, held in Tarquinia, Italy, in June 1997.This book presents, besides three invited surveys, 21 carefully revised full papers selected from 40 presentations given at the workshop. The algebraic approach to the specification and development of systems, born as a formal method for abstract data types, encompases today the formal design of integrated hardware and software systems, new specification frameworks and a wide range of applications. This book presents the state-of-the-art in the area of algebraic software development.

Download or read book Algebraic System Specification and Development written by Michel Bidoit and published by Springer Science & Business Media. This book was released on 1991-06-26 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: Methods for the algebraic specification of abstract data types were proposed in the early 1970s in the USA and Canada and became a major research issue in Europe shortly afterwards. Since then the algebraic approach has come to play a central role in research on formal specification and development, as its range of applications was extended to the specification of complete software systems, to the formal description of the program development process, and to the uniform definition of syntax and semantics of programming languages. Today this approach extends beyond just software to the development of integrated hardware and software systems. These flourishing activities in the area of algebraic specifications have led to an abundance of approaches, theories and concepts, which have universal algebra, category theory and logic as a common mathematical basis. This volume is an annotated bibliography which provides an up-to-date overview of past and present work on algebraic specification. No attempt is made to provide a coherent introduction to the topic for beginners; the intention is rather to provide a guide to the current literature for researchers in algebraic specification and neighboring fields. Some indications of how the different approaches are related are included, together with some ideas concerning possible future directions.

Download or read book Fundamentals of Algebraic Graph Transformation written by Hartmut Ehrig and published by Springer Science & Business Media. This book was released on 2006-05-01 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first textbook treatment of the algebraic approach to graph transformation, based on algebraic structures and category theory. It contains an introduction to classical graphs. Basic and advanced results are first shown for an abstract form of replacement systems and are then instantiated to several forms of graph and Petri net transformation systems. The book develops typed attributed graph transformation and contains a practical case study.

Download or read book Modular Compiler Verification written by Markus Müller-Olm and published by Lecture Notes in Computer Science. This book was released on 1997-08-06 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first comprehensive book on hypermedia and the World Wide Web that includes features of the second generation systems. Definitions, history, current technology and problems, leading-edge initiatives, future applications, all these are seen as an unfolding of a millenial communication medium that is not only serving but also involving even the non-technical person in a very technical world. Much of the promise of hypermedia lies in its applications to education, and this receives prominence in the book. The new hypermedia system HyperWave is described in detail. The book's vision, organization, and easy-to-read style make it suitable as a source of information for the practitioner and the general reader. It may also serve both as a reference book for researchers and as a textbook.

Download or read book Approaches to Algebra written by N. Bednarz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Greek geometry, there is an arithmetic of magnitudes in which, in terms of numbers, only integers are involved. This theory of measure is limited to exact measure. Operations on magnitudes cannot be actually numerically calculated, except if those magnitudes are exactly measured by a certain unit. The theory of proportions does not have access to such operations. It cannot be seen as an "arithmetic" of ratios. Even if Euclidean geometry is done in a highly theoretical context, its axioms are essentially semantic. This is contrary to Mahoney's second characteristic. This cannot be said of the theory of proportions, which is less semantic. Only synthetic proofs are considered rigorous in Greek geometry. Arithmetic reasoning is also synthetic, going from the known to the unknown. Finally, analysis is an approach to geometrical problems that has some algebraic characteristics and involves a method for solving problems that is different from the arithmetical approach. 3. GEOMETRIC PROOFS OF ALGEBRAIC RULES Until the second half of the 19th century, Euclid's Elements was considered a model of a mathematical theory. This may be one reason why geometry was used by algebraists as a tool to demonstrate the accuracy of rules otherwise given as numerical algorithms. It may also be that geometry was one way to represent general reasoning without involving specific magnitudes. To go a bit deeper into this, here are three geometric proofs of algebraic rules, the frrst by Al-Khwarizmi, the other two by Cardano.

Download or read book Algebraic Methodology and Software Technology written by Michael Johnson and published by Springer Science & Business Media. This book was released on 2006-06-27 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the refereed proceedings of the 11th International Conference on Algebraic Methodology and Software Technology. The book collects 24 revised full papers together with 3 system demonstrations and 3 invited talks. Coverage includes current issues in formal methods related to algebraic approaches and to software engineering including abstract data types, process algebras, algebraic specification, model checking, abstraction, refinement, mu-calculus, state machines, rewriting, Kleene algebra, programming logic, and formal software development.