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Eilenberg machines have been introduced in 1974 in the field of formal language theory. They are finite automata for which the alphabet is interpreted by mathematical relations over an abstract set. They generalize many finite state machines. We consider in the present work the subclass of finite Eilenberg machines for which we provide an executable complete simulator. This program is specified using the Coq proof assistant. The correctness of the algorithm is also proved formally anddoi:10.1016/j.entcs.2011.02.019 fatcat:4wgfhaovqjb7pgp6ydh4idqrtm