Robin Bergenthum | Searcharxiv

arXiv2026

Synthesizing Petri Nets from Labelled Petri Nets using Token Trail Regions

Synthesis automatically generates a process model from a behavioural specification. When the target model is a Petri net, we address synthesis through region theory. Researchers have studied region-based synthesis extensively for state-based specifications, such as transition systems and step-transition systems, as well as for language-based specifications. Accordingly, in literature, region theory is divided into two main branches: state-based regions and language-based regions. Using state-based regions, the behavioural specification is a set of global states and related state-transitions. This representation can express conflicts and the merging of global states naturally. However, it suffers from state explosion and can not express concurrency explicitly. Using language-based regions, the behavioural specification is a set of example runs defined by partially or totally ordered sets of events. This representation can express concurrency and branching naturally. However, it grows rapidly with the number of choices and can not express merging of conflicts. So far, synthesis requires a trade-off between these two approaches. Both region definitions have fundamental limitations, and synthesis therefore always involves a compromise. In this paper, we lift these limitations by introducing a new region theory that covers both state-based and language-based input. We prove that the new definition is a region meta theory that combines both concepts. It uses specifications given as a set of labelled nets, which allow us to express conflicts, concurrency and merging of local states naturally, and synthesizes a Petri net that simulates all labelled nets of the input specification.

cs.FL↗

arXiv2025

eST$^2$ Miner -- Process Discovery Based on Firing Partial Orders

Process discovery generates process models from event logs. Traditionally, an event log is defined as a multiset of traces, where each trace is a sequence of events. The total order of the events in a sequential trace is typically based on their temporal occurrence. However, real-life processes are partially ordered by nature. Different activities can occur in different parts of the process and, thus, independently of each other. Therefore, the temporal total order of events does not necessarily reflect their causal order, as also causally unrelated events may be ordered in time. Only partial orders allow to express concurrency, duration, overlap, and uncertainty of events. Consequently, there is a growing need for process mining algorithms that can directly handle partially ordered input. In this paper, we combine two well-established and efficient algorithms, the eST Miner from the process mining community and the Firing LPO algorithm from the Petri net community, to introduce the eST$^2$ Miner. The eST$^2$ Miner is a process discovery algorithm that can directly handle partially ordered input, gives strong formal guarantees, offers good runtime and excellent space complexity, and can, thus, be used in real-life applications.

cs.DB↗