Darren New wrote:
Depends on which analog computer. Most are rather a lot smaller than a Turing machine. Remember the halting problem only exists for infinite-storage computers. Anything with a fixed number of states is "trivial" to check whether it halts.
A modern digital computer has a fixed number of states but given the definition of a program and a finite input is unable to tell you whether that program will run forever or not. The last two sentences of the above paragraph are false. Were they true it would imply that my computer with a mere 4G of RAM is not an infinite-storage computer and can therefore decide the halting problem. It also has a fixed number of states but checking whether a program halts is far from trivial.
Not sure where the halting problem comes in at all, actually.
The human brain can analyze a program and determine whether or not it will ever halt.
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