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Paper
Realization is universal
Abstract
Behavior is left adjoint to minimal realization, as functors between certain categories of machines and behaviors. This gives a succinct characterization of minimal realization valid for discrete as well as linear machines, with or without finiteness condition. Realization theory is therefore expressed in contemporary algebra in a way which reveals its inner structure and suggests generalizations. An adjunction between regular sets and finite state acceptors follows as a corollary. © 1973 Springer-Verlag New York Inc.