Discrete-Event System Model Discovery under Observational Ambiguity: Counterexample Generation via Spectral Learning

Traditional data-driven discrete-event system model discovery using Petri nets often relies on access to both positive examples that describe admissible behavior and counterexamples that rule out forbidden behavior. In industrial settings, however, event logs provide only observed traces, which constitute a partial observation of system behavior, and counterexamples are typically unavailable. This paper addresses counterexample generation from event logs to support labeled Petri net discovery of discrete-event systems. Observed traces provide positive examples, while unobserved alternative events at each step form candidate counterexamples, since non-occurrence does not imply impossibility. We recover a hidden Markov model (HMM) from event logs via a spectral learning approach and use it only as an auxiliary probabilistic model to validate these candidate counterexamples. Beyond counterexample availability, event logs often exhibit observational ambiguity, where the same event label may correspond to multiple underlying system conditions, necessitating labeled Petri nets in which multiple transitions share the same event label. To handle this ambiguity, we formulate labeled Petri net discovery as an integer program and exploit its structure to develop a tailored branch-and-price algorithm. The proposed approach is validated on event logs from LEGO-based laboratory systems and a CNC machining center. Comparisons with process mining techniques show that our approach derives higher-fidelity Petri nets from real manufacturing data, enabling downstream applications such as supervisory control and digital twin deployment in discrete-event systems.