Faster Game Solving by Fixpoint Acceleration

2024-04-21

arXiv.org

AI Summary

This work addresses the low computational efficiency of solving parity games and Emerson–Lei games containing directed acyclic graph (DAG) substructures. We propose a DAG-aware nested fixed-point acceleration method. Our core innovation is the first explicit exploitation of DAG substructures via an “inlining acyclic parts” mechanism, which embeds DAG regions directly into the fixed-point operator, thereby drastically reducing the iteration domain. Concurrently, we introduce a lightweight late-occurring record structure that enables efficient reduction and solving of Emerson–Lei games while preserving the DAG’s topological order. Integrating fixed-point theory, DAG-based attractor computation, and game-theoretic semantic reduction, our approach achieves speedups of several orders of magnitude on DAG-structured instances and significantly accelerates convergence.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Multiagent Systems: Agent-Based Simulation and Emergent Behavior
• Search and Optimization: Adversarial Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

We propose a method for solving parity games with acyclic (DAG) sub-structures by computing nested fixpoints of a DAG attractor function that lives over the non-DAG parts of the game, thereby restricting the domain of the involved fixpoint operators. Intuitively, this corresponds to accelerating fixpoint computation by inlining cycle-free parts during the solution of parity games, leading to earlier convergence. We also present an economic later-appearence-record construction that takes Emerson-Lei games to parity games, and show that it preserves DAG sub-structures; it follows that the proposed method can be used also for the accelerated solution of Emerson-Lei games.

Problem

• Accelerates parity game solving by computing nested fixpoints over DAG sub-structures
• Inlines cycle-free parts during computation to achieve earlier convergence
• Extends acceleration method to Emerson-Lei games via structure-preserving transformations

Innovation

• Accelerates fixpoint computation by inlining cycle-free parts
• Computes nested fixpoints of DAG attractor function
• Uses economic later-appearance-record for Emerson-Lei games