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Coming from a digital functional hardware verification background, I don’t really understand the Halting Problem. I can represent the program as a state machine and show whether all inputs in all states generate a valid output or lead to an infinite loop.
The only requirement is that the inputs and states are finite. E.g. an infinite counter would lead to an infinite number of states.
Since infinite counters or infinite inputs are impossible in reality, does the Halting Problem really have a practical relevance?