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A decision-tree-based approach for correctability of stochastic discrete-event systems

This paper aims to investigate the correctability of stochastic discrete-event systems (DESs) equipped with a probabilistic structure to estimate the likelihood of events occurring. The notion of k-step corrective probability is formalized by using the representation of decision trees to describe the possibility that the stochastic system may recover to accepted states from the current state within k steps. By introducing the strategy of adjusting the transition probability of the current state, a correction mechanism is presented for stochastic systems to achieve the maximal k-step corrective probability. In addition, an approach for the computation of supremal corrective probability is developed by constructing the decision tree after introducing the infinitely expandable states. Finally, an illustrative example is provided.