Introduction to Bisimulation and Coinduction

Author: Davide Sangiorgi

Publisher: Cambridge University Press

ISBN: 1139502832

Category: Computers

Page: N.A

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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

Author: Christos G. Cassandras,Stéphane Lafortune

Publisher: Springer Science & Business Media

ISBN: 0387333320

Category: Technology & Engineering

Page: 772

View: 3325

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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

Author: Prakash Panangaden

Publisher: Imperial College Press

ISBN: 1848162898

Category: Mathematics

Page: 212

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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

Author: Yuxin Deng

Publisher: Springer

ISBN: 3662451980

Category: Computers

Page: 249

View: 321

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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

Author: Davide Sangiorgi,David Walker

Publisher: Cambridge University Press

ISBN: 9780521543279

Category: Computers

Page: 596

View: 4564

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

Mathematical Theory of Computation

Author: Zohar Manna

Publisher: Courier Corporation

ISBN: 9780486152097

Category: Mathematics

Page: 464

View: 5078

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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.

Certified Programming with Dependent Types

A Pragmatic Introduction to the Coq Proof Assistant

Author: Adam Chlipala

Publisher: MIT Press

ISBN: 0262026651

Category: Computers

Page: 424

View: 1010

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

Reactive Systems

Modelling, Specification and Verification

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

Publisher: Cambridge University Press

ISBN: 1139466682

Category: Computers

Page: N.A

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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.

Advanced Topics in Bisimulation and Coinduction

Author: Davide Sangiorgi,Jan Rutten

Publisher: Cambridge University Press

ISBN: 1139502905

Category: Computers

Page: N.A

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Coinduction is a method for specifying and reasoning about infinite data types and automata with infinite behaviour. In recent years, it has come to play an ever more important role in the theory of computing. It is studied in many disciplines, including process theory and concurrency, modal logic and automata theory. Typically, coinductive proofs demonstrate the equivalence of two objects by constructing a suitable bisimulation relation between them. This collection of surveys is aimed at both researchers and Master's students in computer science and mathematics and deals with various aspects of bisimulation and coinduction, with an emphasis on process theory. Seven chapters cover the following topics: history, algebra and coalgebra, algorithmics, logic, higher-order languages, enhancements of the bisimulation proof method, and probabilities. Exercises are also included to help the reader master new material.

Formal Methods for Industrial Critical Systems

20th International Workshop, FMICS 2015 Oslo, Norway, June 22-23, 2015 Proceedings

Author: Manuel Núñez,Matthias Güdemann

Publisher: Springer

ISBN: 3319194585

Category: Computers

Page: 213

View: 9644

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This book constitutes the proceedings of the 20th International Workshop on Formal Methods for Industrial Critical Systems, FMICS 2015, Oslo, Norway, in June 2015. The 12 papers presented in this volume were carefully reviewed and selected from 20 submissions. They are organized in topical sections: applications; protocols; specification and analysis; verification.

Introduction to Process Algebra

Author: Wan Fokkink

Publisher: Springer Science & Business Media

ISBN: 3662042932

Category: Mathematics

Page: 168

View: 818

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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

Author: Jon Barwise,Lawrence Moss

Publisher: Center for the Study of Language and Information Publications

ISBN: 9781575860084

Category: Mathematics

Page: 400

View: 5414

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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.

Software, Services, and Systems

Essays Dedicated to Martin Wirsing on the Occasion of His Retirement from the Chair of Programming and Software Engineering

Author: Rocco De Nicola,Rolf Hennicker

Publisher: Springer

ISBN: 3319155458

Category: Computers

Page: 694

View: 2421

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This book is dedicated to Professor Martin Wirsing on the occasion of his emeritation from Ludwig-Maximilians-Universität in Munich, Germany. The volume is a reflection, with gratitude and admiration, on Professor Wirsing’s life highly creative, remarkably fruitful and intellectually generous life. It also gives a snapshot of the research ideas that in many cases have been deeply influenced by Professor Wirsing’s work. The book consists of six sections. The first section contains personal remembrances and expressions of gratitude from friends of Professor Wirsing. The remaining five sections consist of groups of scientific papers written by colleagues and collaborators of Professor Wirsing, which have been grouped and ordered according to his scientific evolution. More specifically, the papers are concerned with logical and algebraic foundations; algebraic specifications, institutions and rewriting; foundations of software engineering; service oriented systems; and adaptive and autonomic systems.

A Decade of Concurrency

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

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

Publisher: Springer Science & Business Media

ISBN: 9783540580430

Category: Computers

Page: 684

View: 2690

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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.

Modal and Temporal Properties of Processes

Author: Colin Stirling

Publisher: Springer Science & Business Media

ISBN: 1475735502

Category: Technology & Engineering

Page: 191

View: 9620

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In recent years, model checking has become an essential technique for the formal verification of systems. With a clarity of presentation and its many illuminating examples, this book makes this technical material easy to grasp. It is perfectly suited for an advanced undergraduate or graduate class in formal verification and will serve as a valuable resource to practitioners of formal methods.

Advances in Proof Theory

Author: Reinhard Kahle,Thomas Strahm,Thomas Studer

Publisher: Birkhäuser

ISBN: 331929198X

Category: Mathematics

Page: 425

View: 6716

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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.