Process discovery has emerged as a powerful approach to support the analysis and the design of complex processes. It consists of analyzing a set of traces registering the sequence of tasks performed along several enactments of a transactional system, in order to build a process model that can explain all the episodes recorded over them. An approach to accomplish this task is presented that can benefit from the background knowledge that, in many cases, is available to the analysts taking care of the process (re-)design. The approach is based on encoding the information gathered from the log and the (possibly) given background knowledge in terms of precedence constraints , that is, of constraints over the topology of the resulting process models. Mining algorithms are eventually formulated in terms of reasoning problems over precedence constraints, and the computational complexity of such problems is thoroughly analyzed by tracing their tractability frontier. Solution algorithms are proposed and their properties analyzed. These algorithms have been implemented in a prototype system, and results of a thorough experimental activity are discussed.
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