turing-intro.ppt

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turing-intro.ppt

• version 20101123

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Turing 1936On Computable Numbers

• William J. Rapaport
• Department of Computer Science Engineering,
• Department of Philosophy, Department of
  Linguistics,
• and Center for Cognitive Science
• rapaport_at_buffalo.edu
• http//www.cse.buffalo.edu/rapaport

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Hilberts Entscheidungsproblem

• Decision Problem
• ? proposition of math, ?? finite procedure
  (algorithm) that decides its truth-value?
• or that proves/disproves it?
• Possibly
• ? such proposition, ? such a proof/disproof
• but no algorithmic way to find it
• Gödel
• ? true proposition G of arithmetic such that ?
  proof of G

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(No Transcript)
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Turing 1936

• age 24 (!)
• analysis of idealized human computer
• intuitive conception of mechanical calculation
• Euclid ? Leibniz ? Babbage ? Hilbert
• formal mathematical theory (TM)
• convinced Gödel, because of intuitive simplicity
• showed
• intuitive conception ? formal theory ? ?-calculus
• showed Decision Problem unsolvable
• Halting Problem not computable
• existence of Universal TM ( programmable
  computer)