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# Module08 - Module 8 • Halting Problem revisited –...

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1 Module 8 Halting Problem revisited Universal Turing machine half-solves halting problem A universal Turing machine is an operating system/general purpose computer

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2 Half-solving the Halting Problem State the Halting Problem Give an input instance of the Halting Problem We saw last time that the Halting Problem is not solvable. How might we half-solve the Halting Problem?
3 Example Input Program P bool main(unsigned Q) { int i=2; if ((Q = = 0) || (Q= = 1)) return false; while (i<Q) { if (Q%i = = 0) return (false); i++; } return (true); } Nonnegative integer 4

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4 Organization Universal Turing machine’s Memory Program P Program P’s Memory Program P bool main(unsigned Q) { int i=2; if ((Q = = 0) || (Q= = 1)) return false; while (i<Q) { if (Q%i = = 0) return (false); i++; } return (true); } Program Counter int i,Q; 4 Line 1
Description of universal Turing machine * Basic Loop Find current line of program P Execute current line of program P Update program P’s memory

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Module08 - Module 8 • Halting Problem revisited –...

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