Games on Graphs : From Logic and Automata to Algorithms

Fijalkow, ‪Nathanaël (EDT)

Cambridge University Press（2026/04発売）

• 製本 Hardcover:ハードカバー版／ページ数 600 p.
• 言語 ENG
• 商品コード 9781009500685

Full Description

This volume introduces the fundamental results and the state of the art in infinite duration games on graphs. These versatile game models first appeared in the study of automata and logic, but later became important for program verification and synthesis. They have many more applications. In particular, this book covers models from the fields of optimisation, reinforcement learning, model theory, and set theory. The material is presented at a level accessible to beginning graduate students, requiring only a basic understanding of discrete algorithms and graphs. The book's primary objective is constructing efficient algorithms for analysing different types of games. Rather than describe their implementation in full detail, it investigates their theoretical foundations and proves their properties and winning strategies. This tutorial reference from experts across the field is ideal for students, researchers, and professionals in logic and automata, verification and synthesis, and related fields.

Contents

List of contributors; Preface; 1. Introduction Nathanaël Fijalkow; I. Classic: 2. Parity games John Fearnley and Nathanaël Fijalkow; 3. Regular games Nathanael Fijalkow and Florian Horn; 4. Positionality and memory Antonio Casares, Pierre Ohlmann and Pierre Vandenhov; 5. Games with payoffs Nathanaël Fijalkow and Benjamin Monmege; II. Stochastic: 6. Markov decision processes Petr Novotný; 7. Stochastic games Nathalie Betrand, Patricia Bouyer and Nathanaël Fijalkow; III. Information: 8. Concurrent games Rasmus Ibsen-Jensen; 9. Games with signals Hugo Gimbert; 10. Synchronous distributed games C. Aiswarya, Paul Gastin and Nathalie Sznajder; IV. Infinite: 11. Timed games Nicolas Markey and Ocan Sankur; 12. Pushdown games Arnaud Carayol and Olivier Serre; 13. Games with counters Sylvain Schmitz; V. Multi: 14. Games with multiple objectives Mickael Randour; 15. Multiplayer games Romain Brenguier and Ocan Sankue; 16. Bidding games Guy Avni and Thomas A. Henzinger; Bibliography.