Automata and coinduction (an exercise in coalgebra
J. J. M. M. Rutten
P.O. Box 94079, 1090 GB Amsterdam, The Netherlands*
The classical theory of deterministic automata is presented in terms of the notions of homomorphism and bisimulation, which are the cornerstones of the theory of (universal) coalgebra. This leads to a transparent and uniform presentation of automata theory and yields some new insights, amongst which coinduction proof methods for language equality and language inclusion. At the same time, the present treatment of automata theory may serve as an introduction to coalgebra.