Thanks for the fun rabbit hole. They can’t really solve the halting problem though, you can make an oracle solve the halting problem for a turning machine but not for itself. Then of course you can make another oracle machine that solves the halting problem for that oracle machine, and so on and so forth, but an oracle machine can never solve its own halting problem.
They exist in the same grammatical hierarchy so theoretically they can solve the same problems. What I should have said was that nondeterministic turing machines can solve NP problems in P
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Since when were Turing machines ever nondeterministic?
If you augment a TM with nondeterminism, it can still be reduced to a deterministic TM.
Wait till you hear about oracle machines. They can solve any problem, even the halting problem.
(It’s just another mathematical construct that you can do cool things with to prove certain things)
Thanks for the fun rabbit hole. They can’t really solve the halting problem though, you can make an oracle solve the halting problem for a turning machine but not for itself. Then of course you can make another oracle machine that solves the halting problem for that oracle machine, and so on and so forth, but an oracle machine can never solve its own halting problem.
Nondeterministic turing machines are the same kind of impossible theoretical automaton as an NFA. They can theoretically solve NP problems.
It’s been a long long time since I touched this but I’m still almost positive deterministic machines can solve everything in NP already.
They exist in the same grammatical hierarchy so theoretically they can solve the same problems. What I should have said was that nondeterministic turing machines can solve NP problems in P