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In this paper, we consider supervisory control of stochastic discrete eventsystems (SDESs) under linear temporal logic specifications. Applying thebounded synthesis, we reduce the supervisor synthesis into a problem ofsatisfying a safety condition. First, we consider a synthesis problem of adirected controller using the safety condition. We assign a negative reward tothe unsafe states and introduce an expected return with a state-dependentdiscount factor. We compute a winning region and a directed controller with themaximum satisfaction probability using a dynamic programming method, where theexpected return is used as a value function. Next, we construct a permissivesupervisor via the optimal value function. We show that the supervisoraccomplishes the maximum satisfaction probability and maximizes the reachableset within the winning region. Finally, for an unknown SDES, we propose atwo-stage model-free reinforcement learning method for efficient learning ofthe winning region and the directed controllers with the maximum satisfactionprobability. We also demonstrate the effectiveness of the proposed method bysimulation.

Bounded Synthesis and Reinforcement Learning of Supervisors for Stochastic Discrete Event Systems with LTL Specifications