Halting problem within a finite time interval? Let the finite time halting problem to be one where the program is counted as "not halting" if the Turing machine takes more than a given time interval to run the program. 
Is this finite time halting problem undecidable?

In addition to the excellent answer already posted, I'd like to point out some intuition for why it must be computable. 
If you wanted to compute the characteristic function for the finite time halting problem we could run the machine for s steps on the given input. If we assign the value of 1 to problems that have halted in s steps and the value of 0 otherwise, then we have an algorithm that halts on every input.
