Explore the concept of effective theories for computational systems in this lecture from the Santa Fe Institute's 2012 Complex Systems Summer School. Delve into topics such as aggregation, finite state machines, regular languages, and modeling problems. Examine the principles of groups, pure resets, and aggregate rules while considering the aggregation of agents and history models. Investigate the phenomenon of emergence and gain a comprehensive understanding of how these concepts interrelate in complex systems. Benefit from the interdisciplinary approach tailored for graduate and postdoctoral students in mathematical, biological, cognitive, and social sciences.