Question: Prove, using a reduction argument such as given in Section 17.3.2, that the problem of determining whether there is some input on which two arbitrary

Prove, using a reduction argument such as given in Section 17.3.2, that the problem of determining whether there is some input on which two arbitrary programs will both halt is unsolvable.

17.3.2 The Halting Problem Is Unsolvable While there might be intellectual appeal to knowing that there

that the Halting Problem cannot be computed by any computer program. The proof is by contradiction. We begin

1 x |f(x) 1 123456 1 1 1 1 2 3 X 1(X) X 13(x) X |f4(X) 1 2 2 123456 123456... 2 3 4 3 4 5 6 7 9 11 13 15 4 5

17.3.2 The Halting Problem Is Unsolvable While there might be intellectual appeal to knowing that there exists some function that cannot be computed by a computer program, does this mean that there is any such useful function? After all, does it really matter if no program can compute a "nonsense" function such as shown in Bin 4 of Figure 17.5? Now we will prove

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