Topological Duality for Distributive Lattices
Topological Duality for Distributive Lattices
Introducing Stone–Priestley duality theory and its applications to logic and theoretical computer science, this book equips graduate students and researchers with the theoretical background necessary for reading and understanding current research in the area. After giving a thorough introduction to the algebraic, topological, logical, and categorical aspects of the theory, the book covers two advanced applications in computer science, namely in domain theory and automata theory. These topics are at the forefront of active research seeking to unify semantic methods with more algorithmic topics in finite model theory. Frequent exercises punctuate the text, with hints and references provided.
- Provides a concise, self-contained introduction to topological duality methods in logic and computer science, making a very active interdisciplinary field readily available to students and researchers alike
- Contains many exercises ranging from simple ones designed to ensure a good understanding of the material, to more advanced ones uncovering links to further theory
- Covers one of the most emblematic applications of topological duality in computer science, the solution of domain equations from a purely duality-theoretic point of view
- Treats, for the first time in textbook form, the application of Stone–Priestley duality to the theory of regular languages and automata
Reviews & endorsements
'This book introduces efficiently Stone-Priestley duality theory for bounded distributive lattices, thereby laying solid mathematical foundations for applications in mathematics and computer science. Readers interested in the fields of domain theory and automata theory will see the general duality theory bearing fruit and opening doors to further applications.' Jorge Almeida, Universidade do Porto
'This book is a textbook and also a research monograph. For undergraduates there is the basic duality, for postgraduates, applications in algebra, topology and logic, and to theoretical computer science. Then, there are research themes to develop. The applications to CS are exciting and not published as a book before.' Mirna Džamonja, IRIF, CNRS-Université de Paris
'Duality is an indispensable tool in logic and theoretical computer science, and this book provides a great introduction to it. It is very pleasant to read, and does a wonderful job explaining the key ideas. It is highly recommended to anyone entering the field.' Yde Venema, Universiteit van Amsterdam
Product details
March 2024Hardback
9781009349697
367 pages
251 × 175 × 25 mm
0.8kg
Available
Table of Contents
- Preface
- 1. Order and lattices
- 2. Topology and order
- 3. Priestley duality
- 4. Duality methods
- 5. Categorical duality
- 6. Omega-point duality
- 7. Domain theory
- 8. Automata theory
- Bibliography
- Notation
- Index.
