Parity and Exploration Games on Infinite Graphs 1st Edition by Hugo Gimbert – Ebook PDF Instant Download/Delivery. 9783540301240
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ISBN 10:
ISBN 13: 9783540301240
Author: Hugo Gimbert
This paper examines two players’ turn-based perfect-information games played on infinite graphs. Our attention is focused on the classes of games where winning conditions are boolean combinations of the following two conditions: (1) the first one states that an infinite play is won by player 0 if during the play infinitely many different vertices were visited, (2) the second one is the well known parity condition generalized to a countable number of priorities.
We show that, in most cases, both players have positional winning strategies and we characterize their respective winning sets. In the special case of pushdown graphs, we use these results to show that the sets of winning positions are regular and we show how to compute them as well as positional winning strategies in exponential time.
Parity and Exploration Games on Infinite Graphs 1st Table of contents:
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Preliminaries
2.1 Graph Theory Basics
2.2 Infinite Graphs and Their Properties
2.3 Parity Games: Formal Definitions
2.4 Exploration Games: Definitions and Terminology
2.5 Relevant Logic and Automata Theory -
Parity Games on Infinite Graphs
3.1 Formalizing Parity Games on Infinite Graphs
3.2 Strategy Spaces and Winning Conditions
3.3 Complexity of Parity Games
3.4 Decidability and Tractability Results
3.5 Algorithms for Parity Games -
Exploration Games on Infinite Graphs
4.1 Exploration Problems and Setup
4.2 Defining Exploration Games
4.3 Strategy and Winning Conditions in Exploration Games
4.4 Complexity of Exploration Games
4.5 Connection Between Parity and Exploration Games -
Game-Theoretic Approaches to Infinite Graphs
5.1 Strategy Synthesis in Infinite Graphs
5.2 Winning Strategies for Parity and Exploration Games
5.3 Comparison of Strategy Classes
5.4 Applications to Model Checking and Formal Verification -
Decidability and Complexity of Parity and Exploration Games
6.1 Decidability Results for Parity Games on Infinite Graphs
6.2 Complexity Classes and Tractability in Exploration Games
6.3 Reduction Techniques Between Parity and Exploration Games
6.4 Impact of Infinite Graph Structures on Computational Complexity -
Case Studies and Applications
7.1 Parity Games in Verification of Infinite-State Systems
7.2 Exploration Games in Distributed Systems and Robotics
7.3 Game-Theoretic Applications in Control Theory -
Experimental Results and Analysis
8.1 Experimental Setup and Methodology
8.2 Empirical Results on Solving Parity and Exploration Games
8.3 Scalability and Performance Benchmarks
8.4 Comparisons with Related Work -
Challenges and Open Problems
9.1 Limitations of Current Approaches
9.2 Open Problems in Parity Games on Infinite Graphs
9.3 Exploration Games and Real-World Applications
9.4 Future Research Directions
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