Simulation equivalence of automata and circuits

Automata over a symmetric monoidal category M are introduced, and a multi-step simulation is defined among such automata. The collection of M automata is given the structure of a 2-category on the same objects as M , in which the vertical structure is determined by groups of indistinguishable simulations. TwoM -automata are called simulation equivalent if they are connected by an isomorphism of 2-cells in this 2-category. It is shown that the category of simulation equivalent M -automata is monoidal, and it satisfies all the axioms of traced monoidal categories, except the one that explicitly kills the delay.