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

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.