Pfante, OliverOliverPfanteBertschinger, NilsNilsBertschingerOlbrich, EckehardEckehardOlbrichAy, NihatNihatAyJost, JürgenJürgenJost2023-01-052023-01-052014-05-22Advances in Complex Systems 17 (2): 1450007 (2014)http://hdl.handle.net/11420/14500Levels of a complex system are characterized by the fact that they admit a closed functional description in terms of concepts and quantities intrinsic to that level. Several ideas have come up so far in order to make the notion of a closed description precise. In this paper, we present four of these approaches and investigate their mutual relationships. Our study is restricted to the case of discrete dynamical systems, where the different levels are linked by a coarse-graining of variables and states of the system.en0219-525920142World Scientific Publ.aggregated linear dynamicsaggregated Markov chainsaggregation of variablescoarse grainingLumpabilitystate space reductionInformatikJournal Article10.1142/S0219525914500076Other