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Hello =)
If we are to construct a FSM of any kind, do we have to specify zero/null states (Müllzustände) or what is the regulation in this regard?

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I am not sure what you mean with zero/null states (Müllzustände). Are these unreachable states, or states from where we cannot reach the final states? If you mean that, the answer depends on what the exercise is about. If you have to have a deterministic automaton, you probably need these states to maintain the determinism (or you have to minimize the automaton since these states are useless). Otherwise, it may be okay to drop them.
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