Monotonicity-Guided Bottom-Up Petri Net Discovery: The SPECpp Framework

A bottom-up approach to process discovery that exploits monotonic place properties to overcome the exponential candidate space

Leah Tacke genannt Unterberg; Lisa L. Mannel; Wil M. P. van der Aalst· 2026· DOI 10.48550/arXiv.2608.09398

The core problem

Process discovery is one of the central challenges in process mining. Petri nets are particularly attractive because simple local constructs can express complex behavior, including concurrency. While their global behavior may be difficult to analyze, individual places can be efficiently characterized using monotonic properties, enabling bottom-up discovery. Unlike top-down approaches such as the Inductive Miner, which rely on predefined constructs for sequences, choices, loops, and concurrency, the proposed approach allows such structures to emerge organically and can exploit the full expressive power of Petri nets, including free-choice constructs and long-term dependencies. The main challenge is the exponential number of candidate places and their combinations. The authors present the SPECpp framework, which implements strategies to obtain high-quality models under time and resource constraints. SPECpp supports rapid experimentation and is used to evaluate these strategies using both synthetic and real-life event data.

The authors evaluate SPECpp using both synthetic and real-life event data. The synthetic data allows controlled experiments to assess the impact of different strategies on model quality and computation time. Real-life event data tests the framework's applicability in practical settings. The results show that SPECpp can obtain high-quality models under time and resource constraints. The bottom-up approach successfully discovers free-choice constructs and long-term dependencies that top-down methods like the Inductive Miner may miss. The exponential number of candidate places is managed through the implemented strategies, enabling the discovery of complex models without predefined constructs. The framework's ability to support rapid experimentation facilitates the comparison of different strategies and their trade-offs.

Process discovery is one of the central challenges in process mining. Petri nets are particularly attractive because simple local constructs can express complex behavior, including concurrency. While their global behavior may be difficult to analyze, individual places can be efficiently characterized using monotonic properties, enabling bottom-up discovery. Unlike top-down approaches such as the Inductive Miner, which rely on predefined constructs for sequences, choices, loops, and concurrency, the proposed approach allows such structures to emerge organically and can exploit the full expressive power of Petri nets, including free-choice constructs and long-term dependencies. The main challenge is the exponential number of candidate places and their combinations. The authors present the SPECpp framework, which implements strategies to obtain high-quality models under time and resource constraints. SPECpp supports rapid experimentation and is used to evaluate these strategies using both synthetic and real-life event data.

The SPECpp framework adopts a bottom-up discovery strategy. Instead of recursively splitting an event log using predefined process tree constructs, it first identifies candidate places—local Petri net structures—and then combines them into a complete model. The key enabler is the use of monotonic properties to efficiently characterize individual places. A place in a Petri net can be described by its pre-set and post-set of transitions. Monotonicity allows the evaluation of whether a candidate place is valid with respect to the event log without exhaustively checking all possible markings. Formally, for a place p with pre-set ∙ p and post-set p ∙, the place is valid if for every trace σ in the log, the number of times transitions in ∙ p fire before transitions in p ∙ satisfies certain monotonic constraints. The framework implements strategies to handle the exponential number of candidate places and their combinations, including pruning, ranking, and incremental combination. The overall architecture is illustrated below:

The SPECpp framework represents a significant shift from top-down to bottom-up process discovery. By leveraging monotonic properties, it efficiently characterizes individual places, making the exponential candidate space tractable. This allows the discovery of Petri nets that exploit the full expressive power of the formalism, including constructs that are difficult to capture with predefined patterns. The main challenge remains the combinatorial explosion of candidate places and their combinations. The strategies implemented in SPECpp address this by pruning, ranking, and incrementally combining places. The evaluation on synthetic and real-life data demonstrates the framework's effectiveness, but also highlights the need for further research on scalability and the quality of discovered models. The ability to support rapid experimentation is a key strength, enabling researchers to explore different strategies and configurations. Future work may focus on optimizing the combination step and integrating additional monotonic properties to further reduce the search space.

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