Equivalence of Games with Probabilistic Uncertainty and Partial-observation Games

TL;DR

This paper introduces probabilistic uncertainty games, models controller synthesis with imprecise sensors, and shows their equivalence to partial-observation stochastic games, establishing decidability and complexity results.

Contribution

It defines a new class of games with probabilistic uncertainty and proves their polynomial-time reducibility to partial-observation stochastic games, clarifying the decidability landscape.

Findings

Polynomial-time reduction between probabilistic uncertainty games and partial-observation games

Decidability frontier for the new class of games established

Optimal complexity results for most decidable problems

Abstract

We introduce games with probabilistic uncertainty, a natural model for controller synthesis in which the controller observes the state of the system through imprecise sensors that provide correct information about the current state with a fixed probability. That is, in each step, the sensors return an observed state, and given the observed state, there is a probability distribution (due to the estimation error) over the actual current state. The controller must base its decision on the observed state (rather than the actual current state, which it does not know). On the other hand, we assume that the environment can perfectly observe the current state. We show that our model can be reduced in polynomial time to standard partial-observation stochastic games, and vice-versa. As a consequence we establish the precise decidability frontier for the new class of games, and for most of the decidable problems establish optimal complexity results.