Mining structured Petri nets for the visualization of process behavior

Visualization is essential for understanding the models obtained by process mining. Clear and efficient visual representations make the embedded information more accessible and analyzable. This work presents a novel approach for generating process models with structural properties that induce visually friendly layouts. Rather than generating a single model that captures all behaviors, a set of Petri net models is delivered, each one covering a subset of traces of the log. The models are mined by extracting slices of labelled transition systems with specific properties from the complete state space produced by the process logs. In most cases, few Petri nets are sufficient to cover a significant part of the behavior produced by the log.Peer ReviewedPostprint (author's final draft

Learning Hybrid Process Models From Events: Process Discovery Without Faking Confidence

Process discovery techniques return process models that are either formal (precisely describing the possible behaviors) or informal (merely a "picture" not allowing for any form of formal reasoning). Formal models are able to classify traces (i.e., sequences of events) as fitting or non-fitting. Most process mining approaches described in the literature produce such models. This is in stark contrast with the over 25 available commercial process mining tools that only discover informal process models that remain deliberately vague on the precise set of possible traces. There are two main reasons why vendors resort to such models: scalability and simplicity. In this paper, we propose to combine the best of both worlds: discovering hybrid process models that have formal and informal elements. As a proof of concept we present a discovery technique based on hybrid Petri nets. These models allow for formal reasoning, but also reveal information that cannot be captured in mainstream formal models. A novel discovery algorithm returning hybrid Petri nets has been implemented in ProM and has been applied to several real-life event logs. The results clearly demonstrate the advantages of remaining "vague" when there is not enough "evidence" in the data or standard modeling constructs do not "fit". Moreover, the approach is scalable enough to be incorporated in industrial-strength process mining tools.Comment: 25 pages, 12 figure

Discovering duplicate tasks in transition systems for the simplification of process models

This work presents a set of methods to improve the understandability of process models. Traditionally, simplification methods trade off quality metrics, such as fitness or precision. Conversely, the methods proposed in this paper produce simplified models while preserving or even increasing fidelity metrics. The first problem addressed in the paper is the discovery of duplicate tasks. A new method is proposed that avoids overfitting by working on the transition system generated by the log. The method is able to discover duplicate tasks even in the presence of concurrency and choice. The second problem is the structural simplification of the model by identifying optional and repetitive tasks. The tasks are substituted by annotated events that allow the removal of silent tasks and reduce the complexity of the model. An important feature of the methods proposed in this paper is that they are independent from the actual miner used for process discovery.Peer ReviewedPostprint (author's final draft

Event structures for Petri nets with persistence

Event structures are a well-accepted model of concurrency. In a seminal paper by Nielsen, Plotkin and Winskel, they are used to establish a bridge between the theory of domains and the approach to concurrency proposed by Petri. A basic role is played by an unfolding construction that maps (safe) Petri nets into a subclass of event structures, called prime event structures, where each event has a uniquely determined set of causes. Prime event structures, in turn, can be identified with their domain of configurations. At a categorical level, this is nicely formalised by Winskel as a chain of coreflections. Contrary to prime event structures, general event structures allow for the presence of disjunctive causes, i.e., events can be enabled by distinct minimal sets of events. In this paper, we extend the connection between Petri nets and event structures in order to include disjunctive causes. In particular, we show that, at the level of nets, disjunctive causes are well accounted for by persistent places. These are places where tokens, once generated, can be used several times without being consumed and where multiple tokens are interpreted collectively, i.e., their histories are inessential. Generalising the work on ordinary nets, Petri nets with persistence are related to a new subclass of general event structures, called locally connected, by means of a chain of coreflections relying on an unfolding construction

Process windows

We describe a method for formally representing the behaviour of complex processes by process windows. Each window covers a part of the system behaviour, i.e. a part of the underlying transition system, and is easier to understand and analyse than the complete transition system. Process windows can overlap and have shared states and transitions so that the complete system behaviour is the union of window behaviours. We demonstrate the advantage of such representations when dealing with complex system behaviours, and discuss potential applications in circuit design and process mining. As a motivational example we consider the problem of covering transition systems by marked graphs, or more generally choicefree Petri nets. The obtained windows correspond to choice-free behavioural scenarios of the system, wherein one window can take over, or wake up, after another window has become inactive. The corresponding wake-up conditions and wake-up markings can be derived automatically.Peer ReviewedPostprint (author's final draft

Subtyping for Hierarchical, Reconfigurable Petri Nets

Hierarchical Petri nets allow a more abstract view and reconfigurable Petri nets model dynamic structural adaptation. In this contribution we present the combination of reconfigurable Petri nets and hierarchical Petri nets yielding hierarchical structure for reconfigurable Petri nets. Hierarchies are established by substituting transitions by subnets. These subnets are themselves reconfigurable, so they are supplied with their own set of rules. Moreover, global rules that can be applied in all of the net, are provided