Proofofhaltingproblem

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Unformatted text preview: ing that the Towards proving that the Halting Problem is unsolvable… Warm­ups: Self­reference Warm­ups: Self­reference leads to paradox In a certain town, there is a barber who shaves all and only those who don’t shave themselves. Homogenous words: self­describing – “english”, “short”, “polysyllabic”, … Heterogenous words: non­self­describing – “spanish”, “long”, “monosyllabic”, … Warm­ups: Self­reference Warm­ups: Self­reference leads to paradox I can force you to lie, if you answer my question with only “yes” or “no”: Q: Will the next word you say be “no”? “Proof” of Halting problem Suppose there was an algorithm that could tell whether a program halted on given input……(and worked for all inputs) We will show how this leads to a logical contradiction. When an assumption leads to a contradiction, the assumption must be false. “Proof” of Halting problem Suppose there was an algorithm that could tell whether a program halted on given input…… “yes, P(D) halts” program P data D halt­checker “no, P(D) doesn’t halt” Pro...
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This document was uploaded on 04/02/2014.

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