The halting problem concerns programs which take input. By framing the halting problem on the diagonal argument it is clear why this is so.

What about programs with no input, constant functions.

Can it always be determined if they terminate?


1 Answer 1


No, given any program-input pair $(T,x)$ (formally a Turing machine and a word in $\Sigma^*$ for some alphabet $\Sigma$) you can construct a Turing machine with no input that first writes down $x$ and then simulates $T$.

It follows that the problem is undecidable.


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