This work addresses the analysis and characterization of deadlocks in discrete-event systems modeled by labeled Petri nets (LPNs) with undistinguishable and unobservable transitions. To provide a solution for the notorious problem, it is essential to present an effective characterization such that deadlock control and synthesis are technically and methodologically possible. To this end, we introduce the notion of dangerous implicit vectors (DIVs) which implicitly threaten the system deadlock-freedom. The set of dead markings is divided into two subsets: dead basis markings (DBMs) and dangerous implicit markings (DIMs). An algorithm is designed to compute the sets of DIVs and DIMs at a given basis state of a system. Moreover, by virtue of linear algebraic equations, we formulate sufficient conditions to identify the existence of blocking markings in an LPN. Finally, an algorithm is developed to construct an observed graph that is a compact representation of the reachability graph of a Petri net with respect to the existence of dead reaches. At the end of this paper, experiment results that illustrate the correctness and effectiveness of the reported solution are presented.

Many children on the autism spectrum engage in challenging behaviors, like aggression, due to difficulties communicating and regulating their stress. Identifying effective intervention strategies is often subjective and time-consuming. Utilizing unobservable internal physiological data to predict strategy effectiveness may help simplify this process for teachers and parents. This study examined whether heart rate data can predict strategy effectiveness. Teachers and coders from the research team recorded behavioral and heart rate data over three months for each participating student on the autism spectrum using the KeepCalm app, a platform that provides in-the-moment strategy suggestions based on heart rate and past behavioral data, across 226 instances of strategy interventions. A binary logistic regression was performed to assess whether heart rate reduction, time to return to heart rate baseline, and documented skills and challenging behaviors predicted strategy effectiveness. Results suggested that heart rate reduction may be a significant predictor, and supported the existing practice of using behavioral patterns as proxies for strategy effectiveness. Additional analyses indicate proactive strategies are more effective and are associated with greater reduction in heart rate, relative to reactive strategies. Further exploration of how internal physiological data can complement observable behaviors in assessing intervention strategy effectiveness is warranted given the novelty of our findings.