Value Iteration for Stochastic Parity Games

2026-07-20

AI Summary

This work addresses the long-standing lack of efficient value iteration algorithms for the quantitative analysis of stochastic parity games. We propose the first bounded value iteration algorithm that introduces value iteration to the quantitative solution of this problem, circumventing the high computational cost associated with traditional strategy iteration. Our approach leverages a lattice-theoretic characterization of winning probabilities and exploits structural properties of states from which almost-sure victory is achievable under parity objectives, integrating techniques from probabilistic model checking and game-theoretic analysis. We rigorously establish the correctness and convergence of the algorithm, thereby offering a more efficient and scalable method for the quantitative analysis of stochastic parity games.

Abstract

We present the first (bounded) value iteration algorithm for the quantitative analysis of stochastic parity games, a fundamental model for probabilistic verification with $ω$-regular objectives. Existing algorithms are based on strategy iteration, which repeatedly computes optimal strategies for one player while fixing the other, leading to high computational cost. Our algorithm instead operates directly on a lattice-theoretic characterization of winning probabilities, exploiting structural properties of (almost-sure qualitative) winning states under parity objectives. We prove correctness and convergence of the proposed algorithm.

Problem

• stochastic parity games
• value iteration
• quantitative analysis
• probabilistic verification
• ω-regular objectives

Innovation

• value iteration
• stochastic parity games
• quantitative analysis
• lattice-theoretic characterization
• almost-sure winning