Approximating the Value of Energy-Parity Objectives in Simple Stochastic Games

TL;DR

This paper introduces an algorithm to approximate the value of energy-parity objectives in simple stochastic games, balancing quantitative energy constraints with qualitative parity conditions, with complexity bounds and strategy memory requirements.

Contribution

It provides a 2-NEXPTIME algorithm for approximating values and characterizes the memory needed for near-optimal strategies in energy-parity stochastic games.

Findings

Approximation algorithm operates in 2-NEXPTIME.

Strategies require at most exponential memory.

Provides bounds on strategy complexity for energy-parity objectives.

Abstract

We consider simple stochastic games $\mathcal G$ with energy-parity objectives, a combination of quantitative rewards with a qualitative parity condition. The Maximizer tries to avoid running out of energy while simultaneously satisfying a parity condition. We present an algorithm to approximate the value of a given configuration in 2-NEXPTIME. Moreover, $\varepsilon$-optimal strategies for either player require at most $O(2EXP(|{\mathcal G}|)\cdot\log(\frac{1}{\varepsilon}))$ memory modes.