Looking at Mean-Payoff through Foggy Windows

TL;DR

This paper explores window mean-payoff objectives in partial-observation games, demonstrating that some are decidable, unlike classical mean-payoff objectives which are undecidable in this setting.

Contribution

It introduces the decidability of certain window mean-payoff objectives in partial-observation games, contrasting with the undecidability of classical mean-payoff objectives.

Findings

Some window mean-payoff objectives are decidable under partial observation.

Classical mean-payoff objectives remain undecidable with partial observation.

The study provides new insights into quantitative game objectives under limited information.

Abstract

Mean-payoff games (MPGs) are infinite duration two-player zero-sum games played on weighted graphs. Under the hypothesis of perfect information, they admit memoryless optimal strategies for both players and can be solved in NP-intersect-coNP. MPGs are suitable quantitative models for open reactive systems. However, in this context the assumption of perfect information is not always realistic. For the partial-observation case, the problem that asks if the first player has an observation-based winning strategy that enforces a given threshold on the mean-payoff, is undecidable. In this paper, we study the window mean-payoff objectives that were introduced recently as an alternative to the classical mean-payoff objectives. We show that, in sharp contrast to the classical mean-payoff objectives, some of the window mean-payoff objectives are decidable in games with partial-observation.