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Unformatted text preview: X then while 9 < 10 do End (loops) • Build one more program, S: o S reads a program P and duplicates P o Then, S calls Q' with (P, P) as input o P cannot accept itself as input if and only if S halts o That is, P accepts itself as input if and only if S loops forever S: Q': • Lemma 2 : If Q' exists, then S exists • • Theorem 3 : If Q exists, then S halts on input P o iff Q' halts on (P,P) o iff Q' writes out "P does not halt on P" o iff P does not halt on P • • Since S is a syntactically correct program, we can replace P with S in Theorem 3. • Theorem 3' : If Q exists, then S halts on input S o iff Q' halts on (S, S) o iff Q' writes out "S does not halt on S" o iff S does not halt on S A contradiction: Thus, Q can not exist. 2 P P HAL if P doesn’t halt on P then (no op) If P halts on P then while 9 < 10 do End (loops) P...
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 Fall '10
 Dutton
 Halting problem, Alan Turing, syntactically correct program

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