The Fixed Initial Credit Problem for Partial-Observation Energy Games is Ack-complete

TL;DR

This paper investigates a class of two-player partial-observation energy games, proving that determining the fixed initial credit is Ack-complete, highlighting the problem's high computational complexity.

Contribution

The paper establishes that the fixed initial credit problem for partial-observation energy games is Ack-complete, a significant complexity result in this domain.

Findings

The problem is Ack-complete.

Partial observation significantly impacts computational complexity.

The result advances understanding of energy games with asymmetric information.

Abstract

In this paper we study two-player games with asymmetric partial observation and an energy objective. Such games are played on a weighted automaton by Eve, choosing actions, and Adam, choosing a transition labelled with the given action. Eve attempts to maintain the sum of the weights (of the transitions taken) non-negative while Adam tries to do the opposite. Eve does not know the exact state of the game, she is only given an equivalence class of states which contains it. In contrast, Adam has full observation. We show the fixed initial credit problem for these games is Ack-complete.