Suitable ways of putting tolerance structures onto automata are sought. Inertial tolerance on the state set is discussed, but for black box automata an observed or even inertial tolerance on the output set is thought to be more appropriate. Tolerance inductions and coinductions are used to tolerate the remaining two sets in each case. A general definition of a tolerance automaton is suggested and the morphisms of the category defined. The particular case of an (M‐R) automaton is considered and required to yield a stable tolerance structure. Some illustrative examples are given.
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