Topological Duality for Distributive Lattices
Theory and Applications
Author: Mai Gehrke and Sam van Gool Series: Cambridge Tracts in Theoretical Computer Science
Introduces lattice-theoretic and topological methods in logic and computer science, with applications in domain theory and automata theory.
This introduction to Stone–Priestley duality theory brings modern tools in the area together in textbook format for the first time and covers applications to logic and theoretical computer science. This book is for undergraduates, graduate students, and researchers in lattice theory, algebra, topology, logic, and theoretical computer science.
Hardcover
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Summary
Introduces lattice-theoretic and topological methods in logic and computer science, with applications in domain theory and automata theory.
This introduction to Stone–Priestley duality theory brings modern tools in the area together in textbook format for the first time and covers applications to logic and theoretical computer science. This book is for undergraduates, graduate students, and researchers in lattice theory, algebra, topology, logic, and theoretical computer science.
Description
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.
Critic Reviews
'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
About the Author
Mai Gehrke is directeur de recherches in computer science at the French National Centre for Scientific Research (CNRS) working at the department of mathematics of Université Côte d'Azur in Nice. Her main contributions are in Stone duality, canonical extensions, and applications in logic and theoretical computer science. Sam van Gool is maître de conférences at the Research Institute for Foundations of Computer Science (IRIF) at Université Paris Cité. His main contributions are in duality theory and logic in mathematics and computer science.
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