  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.
