An accessible introduction to coalgebra, with clear mathematical explanations and numerous examples and exercises.

A double-pronged approach makes this book an extremely useful addition to the literature on this highly relevant contemporary topic. Addressing two basic areas of application for algebras and coalgebras – as mathematical objects as well as in the context of their application in computer science – the papers cover topics such as abstract models and logics, specialised models and calculi, algebraic and coalgebraic semantics, and system specification and verification. The book is the refereed proceedings of the second CALCO conference, held in August 2007 in Norway.

This book constitutes the refereed proceedings of the First International Conference on Algebra and Coalgebra in Computer Science, CALCO 2005, held in Swansea, UK in September 2005. The biennial conference was created by joining the International Workshop on Coalgebraic Methods in Computer Science (CMCS) and the Workshop on Algebraic Development Techniques (WADT). It addresses two basic areas of application for algebras and coalgebras – as mathematical objects as well as their application in computer science. The 25 revised full papers presented together with 3 invited papers were carefully reviewed and selected from 62 submissions. The papers deal with the following subjects: automata and languages; categorical semantics; hybrid, probabilistic, and timed systems; inductive and coinductive methods; modal logics; relational systems and term rewriting; abstract data types; algebraic and coalgebraic specification; calculi and models of concurrent, distributed, mobile, and context-aware computing; formal testing and quality assurance; general systems theory and computational models (chemical, biological, etc); generative programming and model-driven development; models, correctness and (re)configuration of hardware/middleware/architectures; re-engineering techniques (program transformation); semantics of conceptual modelling methods and techniques; semantics of programming languages; validation and verification.

The purpose of this book is to study the structures needed to model objects in universal algebra, universal coalgebra and theoretical computer science. Universal algebra is used to describe different kinds of algebraic structures, while coalgebras are used to model state-based machines in computer science.The connection between algebras and coalgebras provides a way to connect static data-oriented systems with dynamical behavior-oriented systems. Algebras are used to describe data types and coalgebras describe abstract systems or machines.The book presents a clear overview of the area, from which further study may proceed.

This book constitutes the refereed proceedings of the 5th International Conference on Algebra and Coalgebra in Computer Science, CALCO 2013, held in Warsaw, Poland, in September 2013. The 18 full papers presented together with 4 invited talks were carefully reviewed and selected from 33 submissions. The papers cover topics in the fields of abstract models and logics, specialized models and calculi, algebraic and coalgebraic semantics, system specification and verification, as well as corecursion in programming languages, and algebra and coalgebra in quantum computing. The book also includes 6 papers from the CALCO Tools Workshop, co-located with CALCO 2013 and dedicated to tools based on algebraic and/or coalgebraic principles.

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.