  In this paper, we focus on formal synthesis of control policies for finite
Markov decision processes with non-negative real-valued costs. We develop an
algorithm to automatically generate a policy that guarantees the satisfaction
of a correctness specification expressed as a formula of Linear Temporal Logic,
while at the same time minimizing the expected average cost between two
consecutive satisfactions of a desired property. The existing solutions to this
problem are sub-optimal. By leveraging ideas from automata-based model checking
and game theory, we provide an optimal solution. We demonstrate the approach on
an illustrative example.
