> If memory is finite and the system is deterministic, the program will either halt or repeat a state. The halting problem is thus decidable for non-infinite sy

> If memory is finite and the system is deterministic, the program will either halt or repeat a state. The halting problem is thus decidable for non-infinite systems. While this is theoretically correct, there are offensively short programs for which we can't (yet) decide if they terminate or loop infinitely. E.g. Collatz conjecture offers such a program that does not even require a colossal state to track during execution, its state is one integer. Sadly there are problems that are theoretically decidable but cannot be practically decidable, because the required computation would take the resources of the entire universe, and would take longer than it's projected to exist (at least in a state that can support computation). [1]: https://en.wikipedia.org/wiki/Collatz_conjecture https://en.wikipedia.org/wiki/Collatz_conjecture