Introduction to Coalgebra
Towards Mathematics of States and Observation
Seiten
2016
Cambridge University Press (Verlag)
978-1-107-17789-5 (ISBN)
Cambridge University Press (Verlag)
978-1-107-17789-5 (ISBN)
This is the first mature and accessible introduction to coalgebra, providing clear mathematical explanations, with many examples and exercises involving deterministic and non-deterministic automata, transition systems, streams, Markov chains and weighted automata. It will be of interest to mathematicians, computer scientists, mathematical physicists and even economists.
The area of coalgebra has emerged within theoretical computer science with a unifying claim: to be the mathematics of computational dynamics. It combines ideas from the theory of dynamical systems and from the theory of state-based computation. Although still in its infancy, it is an active area of research that generates wide interest. Written by one of the founders of the field, this book acts as the first mature and accessible introduction to coalgebra. It provides clear mathematical explanations, with many examples and exercises involving deterministic and non-deterministic automata, transition systems, streams, Markov chains and weighted automata. The theory is expressed in the language of category theory, which provides the right abstraction to make the similarity and duality between algebra and coalgebra explicit, and which the reader is introduced to in a hands-on manner. The book will be useful to mathematicians and (theoretical) computer scientists and will also be of interest to mathematical physicists, biologists and economists.
The area of coalgebra has emerged within theoretical computer science with a unifying claim: to be the mathematics of computational dynamics. It combines ideas from the theory of dynamical systems and from the theory of state-based computation. Although still in its infancy, it is an active area of research that generates wide interest. Written by one of the founders of the field, this book acts as the first mature and accessible introduction to coalgebra. It provides clear mathematical explanations, with many examples and exercises involving deterministic and non-deterministic automata, transition systems, streams, Markov chains and weighted automata. The theory is expressed in the language of category theory, which provides the right abstraction to make the similarity and duality between algebra and coalgebra explicit, and which the reader is introduced to in a hands-on manner. The book will be useful to mathematicians and (theoretical) computer scientists and will also be of interest to mathematical physicists, biologists and economists.
Bart Jacobs is Professor of Software and Security Correctness at Radboud University Nijmegen, the Netherlands. His work has been supported by prestigious grants such as the Pionier grant from the Netherlands Organisation for Scientific Research and the Advanced Investigator Grant from the European Research Council. Professor Jacobs is a member of Academia Europaea.
1. Motivation; 2. Coalgebras of polynomial functors; 3. Bisimulations; 4. Logic, lifting and finality; 5. Monads, comonads and distributive laws; 6. Invariants and assertions; References; Definition and symbol index; Subject index.
| Erscheinungsdatum | 20.10.2016 |
|---|---|
| Reihe/Serie | Cambridge Tracts in Theoretical Computer Science |
| Zusatzinfo | Worked examples or Exercises; 11 Line drawings, black and white |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 159 x 235 mm |
| Gewicht | 820 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika |
| Mathematik / Informatik ► Mathematik ► Algebra | |
| ISBN-10 | 1-107-17789-8 / 1107177898 |
| ISBN-13 | 978-1-107-17789-5 / 9781107177895 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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