Advanced Topics In Bisimulation And Coinduction

Author : Davide Sangiorgi
ISBN : 9781139502900
Genre : Computers
File Size : 45.98 MB
Format : PDF, ePub, Mobi

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.
Category: Computers

Introduction To Bisimulation And Coinduction

Author : Davide Sangiorgi
ISBN : 9781139502832
Genre : Computers
File Size : 44.63 MB
Format : PDF, Docs

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.
Category: Computers

Author : Reinhard Kahle
ISBN : 9783319291987
Genre : Mathematics
File Size : 47.63 MB
Format : PDF, ePub, Docs

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.
Category: Mathematics

Theoretical Aspects Of Computing Ictac 2015

Author : Martin Leucker
ISBN : 9783319251509
Genre : Computers
File Size : 21.31 MB
Format : PDF, ePub, Mobi

This book constitutes the refereed proceedings of the 12th International Colloquium on Theoretical Aspects of Computing, ICTAC 2015, held in Cali, Colombia, in October 2015. The 25 revised full papers presented together with 7 invited talks, 3 tool papers, and 2 short papers were carefully reviewed and selected from 93 submissions. The papers cover various topics such as algebra and category theory; automata and formal languages; concurrency; constraints, logic and semantic; software architecture and component-based design; and verification.
Category: Computers

Sofsem 2013 Theory And Practice Of Computer Science

Author : Peter van Emde Boas
ISBN : 9783642358432
Genre : Computers
File Size : 38.19 MB
Format : PDF, ePub, Mobi

This book constitutes the refereed proceedings of the 39th International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2013, held in Špindlerův Mlýn, Czech Republic, in January 2013. The 37 revised full papers presented in this volume were carefully reviewed and selected from 98 submissions. The book also contains 10 invited talks, 5 of which are in full-paper length. The contributions are organized in topical sections named: foundations of computer science; software and Web engineering; data, information, and knowledge engineering; and social computing and human factors.
Category: Computers

Concur 98 Concurrency Theory

Author : Davide Sangiorgi
ISBN : 3540648968
Genre : Computers
File Size : 59.38 MB
Format : PDF, Docs

This book constitutes the refereed proceedings of the 9th International Conference on Concurrency Theory, CONCUR'98, held in Nice, France, in September 1998. The 35 revised full papers presented were carefully selected from a total of 104 submissions. Also presented are five invited contributions. Among the topics covered are moduls of computation and semantic domains, process algebras, Petri Nets, event structures, real-time systems, hybrid systems, model checking, verification techniques, refinement, rewriting, typing systems and algorithms, etc..
Category: Computers

Mathematical Reviews

Author :
ISBN : UOM:39015049327839
Genre : Mathematics
File Size : 54.86 MB
Format : PDF, Docs

Category: Mathematics

The Joy Of Sets

Author : Keith Devlin
ISBN : 0387940944
Genre : Mathematics
File Size : 25.57 MB
Format : PDF, ePub, Mobi

This text covers the parts of contemporary set theory relevant to other areas of pure mathematics. After a review of "naïve" set theory, it develops the Zermelo-Fraenkel axioms of the theory before discussing the ordinal and cardinal numbers. It then delves into contemporary set theory, covering such topics as the Borel hierarchy and Lebesgue measure. A final chapter presents an alternative conception of set theory useful in computer science.
Category: Mathematics

Deutsche Mystik Im Abendl Ndischen Zusammenhang

Author : Walter Haug
ISBN : UOM:39015043199457
Genre : Germany
File Size : 74.6 MB
Format : PDF, Mobi