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Complex Automata were recently proposed as a paradigm to model multi-scale complex systems. The concept is formalized and the scale separation map is further investigated in relation with its capability to specify the components of Complex Automata. Five classes of scale separation are identified, each potentially giving rise to a specific multi-scale modeling paradigm. A number of canonical examples are briefly discussed.

Towards a Complex Automata Framework for Multi-scale Modeling: Formalism and the Scale Separation Map