Process Mining: An iterative algorithm using the Theory of Regions

1. Process Mining: An iterative algorithm using the Theory of Regions Kristian Bisgaard Lassen Boudewijn van Dongen Wil van der Aalst

2. Overview • Introduction to Theory of Regions • Introduction to Process Mining • Applying Theory of Regions to Process Mining • Conclusion

3. Theory of Regions (for Transition Systems) • A Region in a Transition System is a set of states, such that for all transitions in the system holds that: • If that transition enters the region, then all equally labeled transitions enter the region, • If that transition exists the region, then all equally labeled transitions exit the region, • If that transition does not cross the region, then no equally labeled transition crosses the region.

4. Theory of Regions (for Transition Systems) • When all regions are found, a Petri net is built, where these regions correspond to places in the net. • The resulting Petri net is such that its statespace is bisimilar to the transition system that served as input.

5. Process Mining: an overview

6. Log Files • Information systems typically log all kinds of events. We use a XML format for storing event logs. The basic assumption is that the log contains information about specific tasks executed for specific process instances (cases, event-lists, audit trails). Any knowledge of the underlying process is not assumed.

7. Process Mining Event logs Completeness unknown Abstract representation required Theory of Regions State-based models / (regular) languages Complete information provided Exact and compact representation required Big chunks of data, unable to fit in memory. Entire model needs to be present in memory. Completeness of information is very unlikely. Completeness of information is guaranteed by the input model. Main conceptual difference Process Mining VS. Theory of Regions

8. Some existing Process Mining approaches

9. The goal: Applying Theory of Regions in the context of PM Assume an event log is A Transition System, such that each trace starts in a global state

10. Example Log Log: A,B,C,D A,C,B,D A,B,C,D A,C,B,D A,E,D Transition systems

11. Merging the initial state

12. Identifying regions

13. Making the algorithm iterative (i.e. linear in the log)

14. Future work, other approaches • Several other approaches are possible: • Constructing a transition system for the whole log in a smart way: • Rubin et al. propose 36 ways of doing so, but they require the entire transition system to be build in memory. Their approach however can handle “incomplete” information. • Considering the event log as a regular language and use language-based regions as proposed by Darondeau et al. and Lorenz et al.

15. Conclusions • Using our approach, the Theory of Regions can be applied in the context of process mining, in such a way that the approach is linear in the number of cases in the log. • Downsides remain the completeness assumption and the resulting model, since this is not an abstraction of the log, which is often required in process mining.