Introduction to Bisimulation and Coinduction

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Author: Davide Sangiorgi

Publisher: Cambridge University Press

ISBN: 1139502832

Category: Computers

Page: N.A

View: 7070

Induction is a pervasive tool in computer science and mathematics for defining objects and reasoning on them. Coinduction is the dual of induction and as such it brings in quite different tools. Today, it is widely used in computer science, but also in other fields, including artificial intelligence, cognitive science, mathematics, modal logics, philosophy and physics. The best known instance of coinduction is bisimulation, mainly employed to define and prove equalities among potentially infinite objects: processes, streams, non-well-founded sets, etc. This book presents bisimulation and coinduction: the fundamental concepts and techniques and the duality with induction. Each chapter contains exercises and selected solutions, enabling students to connect theory with practice. A special emphasis is placed on bisimulation as a behavioural equivalence for processes. Thus the book serves as an introduction to models for expressing processes (such as process calculi) and to the associated techniques of operational and algebraic analysis.

Introduction to Discrete Event Systems

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Author: Christos G. Cassandras,Stéphane Lafortune

Publisher: Springer Science & Business Media

ISBN: 0387333320

Category: Technology & Engineering

Page: 772

View: 3413

Introduction to Discrete Event Systems is a comprehensive introduction to the field of discrete event systems, offering a breadth of coverage that makes the material accessible to readers of varied backgrounds. The book emphasizes a unified modeling framework that transcends specific application areas, linking the following topics in a coherent manner: language and automata theory, supervisory control, Petri net theory, Markov chains and queuing theory, discrete-event simulation, and concurrent estimation techniques. This edition includes recent research results pertaining to the diagnosis of discrete event systems, decentralized supervisory control, and interval-based timed automata and hybrid automata models.

Labelled Markov Processes

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Author: Prakash Panangaden

Publisher: Imperial College Press

ISBN: 1848162898

Category: Mathematics

Page: 212

View: 9772

Labelled Markov processes are probabilistic versions of labelled transition systems with continuous state spaces. The book covers basic probability and measure theory on continuous state spaces and then develops the theory of LMPs.

Semantics of Probabilistic Processes

An Operational Approach

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Author: Yuxin Deng

Publisher: Springer

ISBN: 3662451980

Category: Computers

Page: 249

View: 5469

This book discusses the semantic foundations of concurrent systems with nondeterministic and probabilistic behaviour. Particular attention is given to clarifying the relationship between testing and simulation semantics and characterising bisimulations from metric, logical, and algorithmic perspectives. Besides presenting recent research outcomes in probabilistic concurrency theory, the book exemplifies the use of many mathematical techniques to solve problems in computer science, which is intended to be accessible to postgraduate students in Computer Science and Mathematics. It can also be used by researchers and practitioners either for advanced study or for technical reference.

The Pi-Calculus

A Theory of Mobile Processes

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Author: Davide Sangiorgi,David Walker

Publisher: Cambridge University Press

ISBN: 9780521543279

Category: Computers

Page: 596

View: 3244

Graduate text on the p-calculus, a mathematical model of mobile computing systems.

Mathematical Theory of Computation

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Author: Zohar Manna

Publisher: Courier Corporation

ISBN: 9780486152097

Category: Mathematics

Page: 464

View: 6444

With the objective of making into a science the art of verifying computer programs (debugging), the author addresses both practical and theoretical aspects of the process. A classic of sequential program verification, this volume has been translated into almost a dozen other languages and is much in demand among graduate and advanced undergraduate computer science students. Subjects include computability (with discussions of finite automata and Turing machines); predicate calculus (basic notions, natural deduction, and the resolution method); verification of programs (both flowchart and algol-like programs); flowchart schemas (basic notions, decision problems, formalization in predicate calculus, and translation programs); and the fixpoint theory of programs (functions and functionals, recursive programs, and verification programs). The treamtent is self-contained, and each chapter concludes with bibliographic remarks, references, and problems.

Reactive Systems

Modelling, Specification and Verification

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Author: Luca Aceto,Anna Ingólfsdóttir,Kim Guldstrand Larsen,Jiri Srba

Publisher: Cambridge University Press

ISBN: 1139466682

Category: Computers

Page: N.A

View: 1989

Formal methods is the term used to describe the specification and verification of software and software systems using mathematical logic. Various methodologies have been developed and incorporated into software tools. An important subclass is distributed systems. There are many books that look at particular methodologies for such systems, e.g. CSP, process algebra. This book offers a more balanced introduction for graduate students that describes the various approaches, their strengths and weaknesses, and when they are best used. Milner's CCS and its operational semantics are introduced, together with notions of behavioural equivalence based on bisimulation techniques and with variants of Hennessy-Milner modal logics. Later in the book, the presented theories are extended to take timing issues into account. The book has arisen from various courses taught in Iceland and Denmark and is designed to give students a broad introduction to the area, with exercises throughout.

Developments in the Design of Thermal Systems

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Author: Robert F. Boehm

Publisher: Cambridge University Press

ISBN: 9780521020053

Category: Science

Page: 308

View: 6423

Reference for engineers in a wide variety of industries (including power plants and chemical plants) on design of thermal systems.

Certified Programming with Dependent Types

A Pragmatic Introduction to the Coq Proof Assistant

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Author: Adam Chlipala

Publisher: MIT Press

ISBN: 0262026651

Category: Computers

Page: 424

View: 7507

A handbook to the Coq software for writing and checking mathematical proofs, with a practical engineering focus.

Introduction to Process Algebra

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Author: Wan Fokkink

Publisher: Springer Science & Business Media

ISBN: 3662042932

Category: Mathematics

Page: 168

View: 7431

Automated and semi-automated manipulation of so-called labelled transition systems has become an important means in discovering flaws in software and hardware systems. Process algebra has been developed to express such labelled transition systems algebraically, which enhances the ways of manipulation by means of equational logic and term rewriting. The theory of process algebra has developed rapidly over the last twenty years, and verification tools have been developed on the basis of process algebra, often in cooperation with techniques related to model checking. This textbook gives a thorough introduction into the basics of process algebra and its applications.

Vicious Circles

On the Mathematics of Non-Wellfounded Phenomena

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Author: Jon Barwise,Lawrence Moss

Publisher: Center for the Study of Language and Information Publications

ISBN: 9781575860084

Category: Mathematics

Page: 400

View: 2690

Circular analyses of philosophical, linguistic, or computational phenomena have been attacked on the assumption that they conflict with mathematical rigour. Barwise and Moss have undertaken to prove this assumption false. This volume is concerned with extending the modelling capabilities of set theory to provide a uniform treatment of circular phenomena. As a means of guiding the reader through the concrete examples of the theory, the authors have included many exercises and solutions: these exercises range in difficulty and ultimately stimulate the reader to come up with new results. Vicious Circles is intended for use by researchers who want to use hypersets; although some experience in mathematics is necessary, the book is accessible to people with widely differing backgrounds and interests.

A Decade of Concurrency

Reflections and Perspectives. REX School/Symposium Noordwijkerhout, The Netherlands, June 1 - 4, 1993. Proceedings

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Author: J.W.de Bakker,W.-P.de Roever,G. Rozenberg

Publisher: Springer Science & Business Media

ISBN: 9783540580430

Category: Computers

Page: 684

View: 4921

The REX School/Symposium "A Decade of Concurrency - Reflections and Perspectives" was the final event of a ten-year period of cooperation between three Dutch research groups working on the foundations of concurrency. Ever since its inception in 1983, the goal of the project has been to contribute to the cross-fertilization between formal methods from the fields of syntax, semantics, and proof theory, aimed at an improved understanding of the nature of parallel computing. The material presented in this volume was prepared by the lecturers (and their coauthors) after the meeting took place. In total, the volume constitutes a thorough state-of-the-art report of the research activities in concurrency.

Advances in Proof Theory

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Author: Reinhard Kahle,Thomas Strahm,Thomas Studer

Publisher: Birkhäuser

ISBN: 331929198X

Category: Mathematics

Page: 425

View: 1983

The aim of this volume is to collect original contributions by the best specialists from the area of proof theory, constructivity, and computation and discuss recent trends and results in these areas. Some emphasis will be put on ordinal analysis, reductive proof theory, explicit mathematics and type-theoretic formalisms, and abstract computations. The volume is dedicated to the 60th birthday of Professor Gerhard Jäger, who has been instrumental in shaping and promoting logic in Switzerland for the last 25 years. It comprises contributions from the symposium “Advances in Proof Theory”, which was held in Bern in December 2013. ​Proof theory came into being in the twenties of the last century, when it was inaugurated by David Hilbert in order to secure the foundations of mathematics. It was substantially influenced by Gödel's famous incompleteness theorems of 1930 and Gentzen's new consistency proof for the axiom system of first order number theory in 1936. Today, proof theory is a well-established branch of mathematical and philosophical logic and one of the pillars of the foundations of mathematics. Proof theory explores constructive and computational aspects of mathematical reasoning; it is particularly suitable for dealing with various questions in computer science.

Functional Programming and Input/Output

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Author: Andrew D. Gordon

Publisher: Cambridge University Press

ISBN: 9780521471039

Category: Computers

Page: 155

View: 6887

Extends functional programming to solve I/O problems, while retaining usual verification features.

Haskell Design Patterns

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Author: Ryan Lemmer

Publisher: Packt Publishing Ltd

ISBN: 1783988738

Category: Computers

Page: 166

View: 1611

Take your Haskell and functional programming skills to the next level by exploring new idioms and design patterns About This Book Explore Haskell on a higher level through idioms and patterns Get an in-depth look into the three strongholds of Haskell: higher-order functions, the Type system, and Lazy evaluation Expand your understanding of Haskell and functional programming, one line of executable code at a time Who This Book Is For If you're a Haskell programmer with a firm grasp of the basics and ready to move more deeply into modern idiomatic Haskell programming, then this book is for you. What You Will Learn Understand the relationship between the “Gang of Four” OOP Design Patterns and Haskell Try out three ways of Streaming I/O: imperative, Lazy, and Iteratee based Explore the pervasive pattern of Composition: from function composition through to high-level composition with Lenses Synthesize Functor, Applicative, Arrow and Monad in a single conceptual framework Follow the grand arc of Fold and Map on lists all the way to their culmination in Lenses and Generic Programming Get a taste of Type-level programming in Haskell and how this relates to dependently-typed programming Retrace the evolution, one key language extension at a time, of the Haskell Type and Kind systems Place the elements of modern Haskell in a historical framework In Detail Design patterns and idioms can widen our perspective by showing us where to look, what to look at, and ultimately how to see what we are looking at. At their best, patterns are a shorthand method of communicating better ways to code (writing less, more maintainable, and more efficient code). This book starts with Haskell 98 and through the lens of patterns and idioms investigates the key advances and programming styles that together make "modern Haskell". Your journey begins with the three pillars of Haskell. Then you'll experience the problem with Lazy I/O, together with a solution. You'll also trace the hierarchy formed by Functor, Applicative, Arrow, and Monad. Next you'll explore how Fold and Map are generalized by Foldable and Traversable, which in turn is unified in a broader context by functional Lenses. You'll delve more deeply into the Type system, which will prepare you for an overview of Generic programming. In conclusion you go to the edge of Haskell by investigating the Kind system and how this relates to Dependently-typed programming. Style and approach Using short pieces of executable code, this guide gradually explores the broad pattern landscape of modern Haskell. Ideas are presented in their historical context and arrived at through intuitive derivations, always with a focus on the problems they solve.

AI for Games and Animation

A Cognitive Modeling Approach

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Author: John David Funge

Publisher: A K Peters/CRC Press

ISBN: 9781568811031

Category: Computers

Page: 288

View: 4720

John Funge introduces a new approach to creating autonomous characters. Cognitive modeling provides computer-animated characters with logic, reasoning, and planning skills. Individual chapters in the book provide concrete examples of advanced character animation, automated cinematography, and a real-time computer game. Source code, animations, images, and other resources are available at the book's website, listed below.

Categories, Allegories

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Author: P.J. Freyd,A. Scedrov

Publisher: Elsevier

ISBN: 9780080887012

Category: Mathematics

Page: 293

View: 1883

General concepts and methods that occur throughout mathematics – and now also in theoretical computer science – are the subject of this book. It is a thorough introduction to Categories, emphasizing the geometric nature of the subject and explaining its connections to mathematical logic. The book should appeal to the inquisitive reader who has seen some basic topology and algebra and would like to learn and explore further. The first part contains a detailed treatment of the fundamentals of Geometric Logic, which combines four central ideas: natural transformations, sheaves, adjoint functors, and topoi. A special feature of the work is a general calculus of relations presented in the second part. This calculus offers another, often more amenable framework for concepts and methods discussed in part one. Some aspects of this approach find their origin in the relational calculi of Peirce and Schroeder from the last century, and in the 1940's in the work of Tarski and others on relational algebras. The representation theorems discussed are an original feature of this approach.