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Título : Handbook of Floating-Point Arithmetic Tipo de documento: documento electrónico Autores: Jean-Michel Muller ; SpringerLink (Online service) ; Nicolas Brisebarre ; Florent de Dinechin ; Claude-Pierre Jeannerod ; Vincent Lefèvre ; Guillaume Melquiond ; Nathalie Revol ; Damien Stehlé ; Serge Torres Editorial: Boston : Birkhäuser Boston Fecha de publicación: 2010 Número de páginas: XXIV, 572 p Il.: online resource ISBN/ISSN/DL: 978-0-8176-4705-6 Idioma : Inglés (eng) Palabras clave: Mathematics Programming languages (Electronic computers) Algorithms Computer science mathematics Applied Engineering Computational and Numerical Analysis Algorithm Problem Complexity Math Applications in Science Appl.Mathematics/Computational Methods of Languages, Compilers, Interpreters Clasificación: 51 Matemáticas Resumen: Floating-point arithmetic is by far the most widely used way of implementing real-number arithmetic on modern computers. Although the basic principles of floating-point arithmetic can be explained in a short amount of time, making such an arithmetic reliable and portable, yet fast, is a very difficult task. From the 1960s to the early 1980s, many different arithmetics were developed, but their implementation varied widely from one machine to another, making it difficult for nonexperts to design, learn, and use the required algorithms. As a result, floating-point arithmetic is far from being exploited to its full potential. This handbook aims to provide a complete overview of modern floating-point arithmetic, including a detailed treatment of the newly revised (IEEE 754-2008) standard for floating-point arithmetic. Presented throughout are algorithms for implementing floating-point arithmetic as well as algorithms that use floating-point arithmetic. So that the techniques presented can be put directly into practice in actual coding or design, they are illustrated, whenever possible, by a corresponding program. Key topics and features include: * Presentation of the history and basic concepts of floating-point arithmetic and various aspects of the past and current standards * Development of smart and nontrivial algorithms, and algorithmic possibilities induced by the availability of a fused multiply-add (fma) instruction, e.g., correctly rounded software division and square roots * Implementation of floating-point arithmetic, either in software—on an integer processor—or hardware, and a discussion of issues related to compilers and languages * Coverage of several recent advances related to elementary functions: correct rounding of these functions and computation of very accurate approximations under constraints * Extensions of floating-point arithmetic such as certification, verification, and big precision Handbook of Floating-Point Arithmetic is designed for programmers of numerical applications, compiler designers, programmers of floating-point algorithms, designers of arithmetic operators, and more generally, students and researchers in numerical analysis who wish to better understand a tool used in their daily work and research. Nota de contenido: Introduction, Basic Definitions, and Standards -- Definitions and Basic Notions -- Floating-Point Formats and Environment -- Cleverly Using Floating-Point Arithmetic -- Basic Properties and Algorithms -- The Fused Multiply-Add Instruction -- Enhanced Floating-Point Sums, Dot Products, and Polynomial Values -- Languages and Compilers -- Implementing Floating-Point Operators -- Algorithms for the Five Basic Operations -- Hardware Implementation of Floating-Point Arithmetic -- Software Implementation of Floating-Point Arithmetic -- Elementary Functions -- Evaluating Floating-Point Elementary Functions -- Solving the Table Maker’s Dilemma -- Extensions -- Formalisms for Certifying Floating-Point Algorithms -- Extending the Precision -- Perspectives and Appendix -- Conclusion and Perspectives -- Appendix: Number Theory Tools for Floating-Point Arithmetic En línea: http://dx.doi.org/10.1007/978-0-8176-4705-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33538 Handbook of Floating-Point Arithmetic [documento electrónico] / Jean-Michel Muller ; SpringerLink (Online service) ; Nicolas Brisebarre ; Florent de Dinechin ; Claude-Pierre Jeannerod ; Vincent Lefèvre ; Guillaume Melquiond ; Nathalie Revol ; Damien Stehlé ; Serge Torres . - Boston : Birkhäuser Boston, 2010 . - XXIV, 572 p : online resource.
ISBN : 978-0-8176-4705-6
Idioma : Inglés (eng)
Palabras clave: Mathematics Programming languages (Electronic computers) Algorithms Computer science mathematics Applied Engineering Computational and Numerical Analysis Algorithm Problem Complexity Math Applications in Science Appl.Mathematics/Computational Methods of Languages, Compilers, Interpreters Clasificación: 51 Matemáticas Resumen: Floating-point arithmetic is by far the most widely used way of implementing real-number arithmetic on modern computers. Although the basic principles of floating-point arithmetic can be explained in a short amount of time, making such an arithmetic reliable and portable, yet fast, is a very difficult task. From the 1960s to the early 1980s, many different arithmetics were developed, but their implementation varied widely from one machine to another, making it difficult for nonexperts to design, learn, and use the required algorithms. As a result, floating-point arithmetic is far from being exploited to its full potential. This handbook aims to provide a complete overview of modern floating-point arithmetic, including a detailed treatment of the newly revised (IEEE 754-2008) standard for floating-point arithmetic. Presented throughout are algorithms for implementing floating-point arithmetic as well as algorithms that use floating-point arithmetic. So that the techniques presented can be put directly into practice in actual coding or design, they are illustrated, whenever possible, by a corresponding program. Key topics and features include: * Presentation of the history and basic concepts of floating-point arithmetic and various aspects of the past and current standards * Development of smart and nontrivial algorithms, and algorithmic possibilities induced by the availability of a fused multiply-add (fma) instruction, e.g., correctly rounded software division and square roots * Implementation of floating-point arithmetic, either in software—on an integer processor—or hardware, and a discussion of issues related to compilers and languages * Coverage of several recent advances related to elementary functions: correct rounding of these functions and computation of very accurate approximations under constraints * Extensions of floating-point arithmetic such as certification, verification, and big precision Handbook of Floating-Point Arithmetic is designed for programmers of numerical applications, compiler designers, programmers of floating-point algorithms, designers of arithmetic operators, and more generally, students and researchers in numerical analysis who wish to better understand a tool used in their daily work and research. Nota de contenido: Introduction, Basic Definitions, and Standards -- Definitions and Basic Notions -- Floating-Point Formats and Environment -- Cleverly Using Floating-Point Arithmetic -- Basic Properties and Algorithms -- The Fused Multiply-Add Instruction -- Enhanced Floating-Point Sums, Dot Products, and Polynomial Values -- Languages and Compilers -- Implementing Floating-Point Operators -- Algorithms for the Five Basic Operations -- Hardware Implementation of Floating-Point Arithmetic -- Software Implementation of Floating-Point Arithmetic -- Elementary Functions -- Evaluating Floating-Point Elementary Functions -- Solving the Table Maker’s Dilemma -- Extensions -- Formalisms for Certifying Floating-Point Algorithms -- Extending the Precision -- Perspectives and Appendix -- Conclusion and Perspectives -- Appendix: Number Theory Tools for Floating-Point Arithmetic En línea: http://dx.doi.org/10.1007/978-0-8176-4705-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33538 Ejemplares
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Título : A Course in Formal Languages, Automata and Groups Tipo de documento: documento electrónico Autores: Ian M. Chiswell ; SpringerLink (Online service) Editorial: London : Springer London Fecha de publicación: 2009 Colección: Universitext, ISSN 0172-5939 Número de páginas: IX, 157 p. 30 illus Il.: online resource ISBN/ISSN/DL: 978-1-84800-940-0 Idioma : Inglés (eng) Palabras clave: Mathematics Mathematical logic Category theory (Mathematics) Homological algebra Group Algebraic topology Manifolds Complex manifolds Theory and Generalizations Logic Formal Languages Topology Cell Complexes (incl. Diff.Topology) Theory, Algebra Clasificación: 51 Matemáticas Resumen: Based on the author’s lecture notes for an MSc course, this text combines formal language and automata theory and group theory, a thriving research area that has developed extensively over the last twenty-five years. The aim of the first three chapters is to give a rigorous proof that various notions of recursively enumerable language are equivalent. Chapter One begins with languages defined by Chomsky grammars and the idea of machine recognition, contains a discussion of Turing Machines, and includes work on finite state automata and the languages they recognise. The following chapters then focus on topics such as recursive functions and predicates; recursively enumerable sets of natural numbers; and the group-theoretic connections of language theory, including a brief introduction to automatic groups. Highlights include: A comprehensive study of context-free languages and pushdown automata in Chapter Four, in particular a clear and complete account of the connection between LR(k) languages and deterministic context-free languages. A self-contained discussion of the significant Muller-Schupp result on context-free groups. Enriched with precise definitions, clear and succinct proofs and worked examples, the book is aimed primarily at postgraduate students in mathematics but will also be of great interest to researchers in mathematics and computer science who want to learn more about the interplay between group theory and formal languages. A solutions manual is available to instructors via www.springer.com Nota de contenido: Preface -- Contents -- 1. Grammars and Machine Recognition -- 2. Recursive Functions -- 3. Recursively Enumerable Sets and Languages -- 4. Context-free language -- 5. Connections with Group Theory -- A. Results and Proofs Omitted in the Text -- B. The Halting Problem and Universal Turing Machines -- C. Cantor's Diagonal Argument -- D. Solutions to Selected Exercises -- References -- Index En línea: http://dx.doi.org/10.1007/978-1-84800-940-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33981 A Course in Formal Languages, Automata and Groups [documento electrónico] / Ian M. Chiswell ; SpringerLink (Online service) . - London : Springer London, 2009 . - IX, 157 p. 30 illus : online resource. - (Universitext, ISSN 0172-5939) .
ISBN : 978-1-84800-940-0
Idioma : Inglés (eng)
Palabras clave: Mathematics Mathematical logic Category theory (Mathematics) Homological algebra Group Algebraic topology Manifolds Complex manifolds Theory and Generalizations Logic Formal Languages Topology Cell Complexes (incl. Diff.Topology) Theory, Algebra Clasificación: 51 Matemáticas Resumen: Based on the author’s lecture notes for an MSc course, this text combines formal language and automata theory and group theory, a thriving research area that has developed extensively over the last twenty-five years. The aim of the first three chapters is to give a rigorous proof that various notions of recursively enumerable language are equivalent. Chapter One begins with languages defined by Chomsky grammars and the idea of machine recognition, contains a discussion of Turing Machines, and includes work on finite state automata and the languages they recognise. The following chapters then focus on topics such as recursive functions and predicates; recursively enumerable sets of natural numbers; and the group-theoretic connections of language theory, including a brief introduction to automatic groups. Highlights include: A comprehensive study of context-free languages and pushdown automata in Chapter Four, in particular a clear and complete account of the connection between LR(k) languages and deterministic context-free languages. A self-contained discussion of the significant Muller-Schupp result on context-free groups. Enriched with precise definitions, clear and succinct proofs and worked examples, the book is aimed primarily at postgraduate students in mathematics but will also be of great interest to researchers in mathematics and computer science who want to learn more about the interplay between group theory and formal languages. A solutions manual is available to instructors via www.springer.com Nota de contenido: Preface -- Contents -- 1. Grammars and Machine Recognition -- 2. Recursive Functions -- 3. Recursively Enumerable Sets and Languages -- 4. Context-free language -- 5. Connections with Group Theory -- A. Results and Proofs Omitted in the Text -- B. The Halting Problem and Universal Turing Machines -- C. Cantor's Diagonal Argument -- D. Solutions to Selected Exercises -- References -- Index En línea: http://dx.doi.org/10.1007/978-1-84800-940-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33981 Ejemplares
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Título : A Course on Mathematical Logic Tipo de documento: documento electrónico Autores: Shashi Mohan Srivastava ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2013 Otro editor: Imprint: Springer Colección: Universitext, ISSN 0172-5939 Número de páginas: XII, 198 p Il.: online resource ISBN/ISSN/DL: 978-1-4614-5746-6 Idioma : Inglés (eng) Palabras clave: Mathematics Mathematical logic Algebra Logic and Foundations Formal Languages Clasificación: 51 Matemáticas Resumen: This is a short, modern, and motivated introduction to mathematical logic for upper undergraduate and beginning graduate students in mathematics and computer science. Any mathematician who is interested in getting acquainted with logic and would like to learn Gödel’s incompleteness theorems should find this book particularly useful. The treatment is thoroughly mathematical and prepares students to branch out in several areas of mathematics related to foundations and computability, such as logic, axiomatic set theory, model theory, recursion theory, and computability. In this new edition, many small and large changes have been made throughout the text. The main purpose of this new edition is to provide a healthy first introduction to model theory, which is a very important branch of logic. Topics in the new chapter include ultraproduct of models, elimination of quantifiers, types, applications of types to model theory, and applications to algebra, number theory and geometry. Some proofs, such as the proof of the very important completeness theorem, have been completely rewritten in a more clear and concise manner. The new edition also introduces new topics, such as the notion of elementary class of structures, elementary diagrams, partial elementary maps, homogeneous structures, definability, and many more. Review from the first edition: "All results included in the book are very carefully selected and proved. The author’s manner of writing is excellent, which will surely make this book useful to many categories of readers." --Marius Tarnauceanu, Zentralblatt MATH Nota de contenido: Preface -- 1 Syntax of First-Order Logic -- 2 Semantics of First-Order Languages -- 3 Propositional Logic -- 4 Completeness Theorem for First-Order Logic -- 5 Model Theory -- 6 Recursive Functions and Arithmetization of Theories -- 7 Incompleteness Theorems and Recursion Theory -- References -- Index En línea: http://dx.doi.org/10.1007/978-1-4614-5746-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32268 A Course on Mathematical Logic [documento electrónico] / Shashi Mohan Srivastava ; SpringerLink (Online service) . - New York, NY : Springer New York : Imprint: Springer, 2013 . - XII, 198 p : online resource. - (Universitext, ISSN 0172-5939) .
ISBN : 978-1-4614-5746-6
Idioma : Inglés (eng)
Palabras clave: Mathematics Mathematical logic Algebra Logic and Foundations Formal Languages Clasificación: 51 Matemáticas Resumen: This is a short, modern, and motivated introduction to mathematical logic for upper undergraduate and beginning graduate students in mathematics and computer science. Any mathematician who is interested in getting acquainted with logic and would like to learn Gödel’s incompleteness theorems should find this book particularly useful. The treatment is thoroughly mathematical and prepares students to branch out in several areas of mathematics related to foundations and computability, such as logic, axiomatic set theory, model theory, recursion theory, and computability. In this new edition, many small and large changes have been made throughout the text. The main purpose of this new edition is to provide a healthy first introduction to model theory, which is a very important branch of logic. Topics in the new chapter include ultraproduct of models, elimination of quantifiers, types, applications of types to model theory, and applications to algebra, number theory and geometry. Some proofs, such as the proof of the very important completeness theorem, have been completely rewritten in a more clear and concise manner. The new edition also introduces new topics, such as the notion of elementary class of structures, elementary diagrams, partial elementary maps, homogeneous structures, definability, and many more. Review from the first edition: "All results included in the book are very carefully selected and proved. The author’s manner of writing is excellent, which will surely make this book useful to many categories of readers." --Marius Tarnauceanu, Zentralblatt MATH Nota de contenido: Preface -- 1 Syntax of First-Order Logic -- 2 Semantics of First-Order Languages -- 3 Propositional Logic -- 4 Completeness Theorem for First-Order Logic -- 5 Model Theory -- 6 Recursive Functions and Arithmetization of Theories -- 7 Incompleteness Theorems and Recursion Theory -- References -- Index En línea: http://dx.doi.org/10.1007/978-1-4614-5746-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32268 Ejemplares
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Título : The Pillars of Computation Theory : State, Encoding, Nondeterminism Tipo de documento: documento electrónico Autores: Arnold L. Rosenberg ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2010 Colección: Universitext, ISSN 0172-5939 Número de páginas: XVIII, 326 p. 49 illus Il.: online resource ISBN/ISSN/DL: 978-0-387-09639-1 Idioma : Inglés (eng) Palabras clave: Computer science Computers Algorithms Mathematical logic Mathematics Science Theory of Computation Computing Algorithm Analysis and Problem Complexity Logic Foundations by Abstract Devices Formal Languages Clasificación: 51 Matemáticas Resumen: Computation theory is a discipline that strives to use mathematical tools and concepts in order to expose the nature of the activity that we call “computation” and to explain a broad range of observed computational phenomena. Why is it harder to perform some computations than others? Are the differences in difficulty that we observe inherent, or are they artifacts of the way we try to perform the computations? Even more basically: how does one reason about such questions? This book strives to endow upper-level undergraduate students and lower-level graduate students with the conceptual and manipulative tools necessary to make Computation theory part of their professional lives. The author tries to achieve this goal via three stratagems that set this book apart from most other texts on the subject. (1) The author develops the necessary mathematical concepts and tools from their simplest instances, so that the student has the opportunity to gain operational control over the necessary mathematics. (2) He organizes the development of the theory around the three “pillars” that give the book its name, so that the student sees computational topics that have the same intellectual origins developed in physical proximity to one another. (3) He strives to illustrate the “big ideas” that computation theory is built upon with applications of these ideas within “practical” domains that the students have seen elsewhere in their courses, in mathematics, in computer science, and in computer engineering Nota de contenido: PROLEGOMENA -- Mathematical Preliminaries -- STATE -- Online Automata: Exemplars of #x201C;State#x201D; -- Finite Automata and Regular Languages -- Applications of the Myhill#x2013;Nerode Theorem -- Enrichment Topics -- ENCODING -- Countability and Uncountability: The Precursors of #x201C;Encoding#x201D; -- Enrichment Topic: #x201C;Efficient#x201D; Pairing Functions, with Applications -- Computability Theory -- NONDETERMINISM -- Nondeterministic Online Automata -- Nondeterministic FAs -- Nondeterminism in Computability Theory -- Complexity Theory En línea: http://dx.doi.org/10.1007/978-0-387-09639-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33493 The Pillars of Computation Theory : State, Encoding, Nondeterminism [documento electrónico] / Arnold L. Rosenberg ; SpringerLink (Online service) . - New York, NY : Springer New York, 2010 . - XVIII, 326 p. 49 illus : online resource. - (Universitext, ISSN 0172-5939) .
ISBN : 978-0-387-09639-1
Idioma : Inglés (eng)
Palabras clave: Computer science Computers Algorithms Mathematical logic Mathematics Science Theory of Computation Computing Algorithm Analysis and Problem Complexity Logic Foundations by Abstract Devices Formal Languages Clasificación: 51 Matemáticas Resumen: Computation theory is a discipline that strives to use mathematical tools and concepts in order to expose the nature of the activity that we call “computation” and to explain a broad range of observed computational phenomena. Why is it harder to perform some computations than others? Are the differences in difficulty that we observe inherent, or are they artifacts of the way we try to perform the computations? Even more basically: how does one reason about such questions? This book strives to endow upper-level undergraduate students and lower-level graduate students with the conceptual and manipulative tools necessary to make Computation theory part of their professional lives. The author tries to achieve this goal via three stratagems that set this book apart from most other texts on the subject. (1) The author develops the necessary mathematical concepts and tools from their simplest instances, so that the student has the opportunity to gain operational control over the necessary mathematics. (2) He organizes the development of the theory around the three “pillars” that give the book its name, so that the student sees computational topics that have the same intellectual origins developed in physical proximity to one another. (3) He strives to illustrate the “big ideas” that computation theory is built upon with applications of these ideas within “practical” domains that the students have seen elsewhere in their courses, in mathematics, in computer science, and in computer engineering Nota de contenido: PROLEGOMENA -- Mathematical Preliminaries -- STATE -- Online Automata: Exemplars of #x201C;State#x201D; -- Finite Automata and Regular Languages -- Applications of the Myhill#x2013;Nerode Theorem -- Enrichment Topics -- ENCODING -- Countability and Uncountability: The Precursors of #x201C;Encoding#x201D; -- Enrichment Topic: #x201C;Efficient#x201D; Pairing Functions, with Applications -- Computability Theory -- NONDETERMINISM -- Nondeterministic Online Automata -- Nondeterministic FAs -- Nondeterminism in Computability Theory -- Complexity Theory En línea: http://dx.doi.org/10.1007/978-0-387-09639-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33493 Ejemplares
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Título : Instruction Sequences for Computer Science Tipo de documento: documento electrónico Autores: Jan A. Bergstra ; SpringerLink (Online service) ; Cornelis A. Middelburg Editorial: Paris : Atlantis Press Fecha de publicación: 2012 Colección: Atlantis Studies in Computing, ISSN 2212-8557 num. 2 Número de páginas: XVI, 232 p Il.: online resource ISBN/ISSN/DL: 978-94-91216-65-7 Idioma : Inglés (eng) Palabras clave: Computer science organization Programming languages (Electronic computers) Computers logic Mathematical Science Computation by Abstract Devices Logics and Meanings of Programs Logic Formal Languages Languages, Compilers, Interpreters Systems Organization Communication Networks Clasificación: 51 Matemáticas Resumen: This book demonstrates that the concept of an instruction sequence offers a novel and useful viewpoint on issues relating to diverse subjects in computer science. Selected issues relating to well-known subjects from the theory of computation and the area of computer architecture are rigorously investigated in this book thinking in terms of instruction sequences. The subjects from the theory of computation, to wit the halting problem and non-uniform computational complexity, are usually investigated thinking in terms of a common model of computation such as Turing machines and Boolean circuits. The subjects from the area of computer architecture, to wit instruction sequence performance, instruction set architectures and remote instruction processing, are usually not investigated in a rigorous way at all Nota de contenido: Introduction -- Instruction Sequences -- Instruction Processing -- Expressiveness of Instruction Sequences -- Computation-Theoretic Issues -- Computer-Architectural Issues -- Instruction Sequences and Process Algebra -- Variations on a Theme -- Appendix A: Five Challenges for Projectionism -- Appendix B: Natural Number Functional Units -- Appendix C: Dynamically Instantiated Instructions -- Appendix D: Analytic Execution Architectures En línea: http://dx.doi.org/10.2991/978-94-91216-65-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33067 Instruction Sequences for Computer Science [documento electrónico] / Jan A. Bergstra ; SpringerLink (Online service) ; Cornelis A. Middelburg . - Paris : Atlantis Press, 2012 . - XVI, 232 p : online resource. - (Atlantis Studies in Computing, ISSN 2212-8557; 2) .
ISBN : 978-94-91216-65-7
Idioma : Inglés (eng)
Palabras clave: Computer science organization Programming languages (Electronic computers) Computers logic Mathematical Science Computation by Abstract Devices Logics and Meanings of Programs Logic Formal Languages Languages, Compilers, Interpreters Systems Organization Communication Networks Clasificación: 51 Matemáticas Resumen: This book demonstrates that the concept of an instruction sequence offers a novel and useful viewpoint on issues relating to diverse subjects in computer science. Selected issues relating to well-known subjects from the theory of computation and the area of computer architecture are rigorously investigated in this book thinking in terms of instruction sequences. The subjects from the theory of computation, to wit the halting problem and non-uniform computational complexity, are usually investigated thinking in terms of a common model of computation such as Turing machines and Boolean circuits. The subjects from the area of computer architecture, to wit instruction sequence performance, instruction set architectures and remote instruction processing, are usually not investigated in a rigorous way at all Nota de contenido: Introduction -- Instruction Sequences -- Instruction Processing -- Expressiveness of Instruction Sequences -- Computation-Theoretic Issues -- Computer-Architectural Issues -- Instruction Sequences and Process Algebra -- Variations on a Theme -- Appendix A: Five Challenges for Projectionism -- Appendix B: Natural Number Functional Units -- Appendix C: Dynamically Instantiated Instructions -- Appendix D: Analytic Execution Architectures En línea: http://dx.doi.org/10.2991/978-94-91216-65-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33067 Ejemplares
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