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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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