Decomposed process discovery and decomposed conformance checking are the corresponding variants of the two monolithic fundamental problems in process mining (van der Aalst 2011): automated process discovery, which considers the problem of discovering a process model from an event log (Leemans 2009), and conformance checking, which addresses the problem of analyzing the adequacy of a process model with respect to observed behavior (Munoz-Gama 2009), respectively. The term decomposed in the two definitions is mainly describing the way the two problems are tackled operationally, to face their computational complexity by splitting the initial problem into smaller problems, that can be solved individually and often more efficiently.Postprint ...