Process Discovery with Precedence Constraints

The automatic discovery of a process model out of a historical log traces can be of great value for both analysis and design tasks, and is a major goal of Process Mining approaches. A key step in discovering such a model consists in detecting a graph of causal/precedence dependencies over process activities – which can be possibly used to eventually derive more expressive control-flow (e.g., Petri-net based) models. To this end, most of current approaches exploit greedy heuristics and discard apriori some dependencies assuming that the given log is complete (i.e., it covers the possible behavior of the process) – so risking to be ineffective when working with high-concurrency processes and with noisy and temporally-biased logs. Despite the usage of a-priori knowledge could improve the effectiveness, efficiency and robustness (w.r.t. incomplete/noisy data) of dependency mining algorithms, it has been given little attention so far. This paper fills the gap by proposing a constraint-based process discovery framework, where background knowledge can be encoded via precedence constraints, while the search of dependencies can be encoded as either a constraints satisfaction or a constraints satisfaction optimization problem. The computational complexity of such problems is studied deeply, and their tractability frontier is traced w.r.t. the different classes of constraints involved. The whole approach has been implemented in a prototype system, leveraging on a solid constraint programming platform, and tested on both synthesized and real log data.