  This paper studies the synthesis of control policies for an agent that has to
satisfy a temporal logic specification in a partially observable environment,
in the presence of an adversary. The interaction of the agent (defender) with
the adversary is modeled as a partially observable stochastic game. The goal is
to generate a defender policy to maximize satisfaction of a given temporal
logic specification under any adversary policy. The search for policies is
limited to the space of finite state controllers, which leads to a tractable
approach to determine policies. We relate the satisfaction of the specification
to reaching (a subset of) recurrent states of a Markov chain. We present an
algorithm to determine a set of defender and adversary finite state controllers
of fixed sizes that will satisfy the temporal logic specification, and prove
that it is sound. We then propose a value-iteration algorithm to maximize the
probability of satisfying the temporal logic specification under finite state
controllers of fixed sizes. Lastly, we extend this setting to the scenario
where the size of the finite state controller of the defender can be increased
to improve the satisfaction probability. We illustrate our approach with an
example.
