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Rage against the Turing Machine

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Programming is hard

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while (!in_array($state, $accept_states)) { $read_val = isset($tape[$position]) ? $tape[$position] : '_'; ! if (!isset($rules[$state][$read_val])) { throw new NoTransitionException(); } ! list($write_val, $move_dir, $new_state) = $rules[$state][$read_val]; ! $tape[$position] = $write_val; ! if ('l' === $move_dir) { $position--; if ($position < 0) { $position++; array_unshift($tape, '_'); } } else if ('r' === $move_dir) { $position++; if ($position >= count($tape)) { array_push($tape, '_'); } } ! $state = $new_state; }

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This machine can run any algorithm

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This machine can run any algorithm etsy.com/shop/sharpwriter

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Universality

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add increment one-third

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add increment one-third add increment one-third

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add increment one-third

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add increment one-third U

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U M

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Entscheidungsproblem

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Halts?

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Halts? Negate

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Halts? Negate Copy

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Halts? Negate Copy { X

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( ) X X

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Halts? Negate Copy X

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Halts? Negate Copy X X

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Halts? Negate Copy true X X

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Halts? Negate Copy X ∞ true X

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Halts? Negate Copy X ∞ true X X X }

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Halts? Negate Copy false X X

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Halts? Negate Copy false halting now X X

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Halts? Negate Copy false halting now X X X X }

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• Proof by contradiction • Decision machine cannot exist • We are screwed

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How to cope

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• Restricted subsets of computing • Finite state machines • Type systems

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Conclusion

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Programming is hard