100 lines
4.1 KiB
Markdown
100 lines
4.1 KiB
Markdown
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## \-\-- Day 25: The Halting Problem \-\--
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Following the twisty passageways deeper and deeper into the CPU, you
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finally reach the core of the computer.
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Here, in the expansive central chamber, you find a grand apparatus that
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fills the entire room, suspended nanometers above your head.
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You had always imagined CPUs to be noisy, chaotic places, bustling with
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activity. Instead, the room is quiet, motionless, and dark.
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Suddenly, you and the CPU\'s *garbage collector* startle each other.
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\"It\'s not often we get many visitors here!\", he says. You inquire
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about the stopped machinery.
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\"It stopped milliseconds ago; not sure why. I\'m a garbage collector,
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not a doctor.\" You ask what the machine is for.
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\"Programs these days, don\'t know their origins. That\'s the *Turing
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machine*! It\'s what makes the whole computer work.\" You try to explain
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that Turing machines are merely models of computation, but he cuts you
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off. \"No, see, that\'s just what they *want* you to think. Ultimately,
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inside every CPU, there\'s a Turing machine driving the whole thing! Too
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bad this one\'s broken. [We\'re
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doomed!](https://www.youtube.com/watch?v=cTwZZz0HV8I)\"
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You ask how you can help. \"Well, unfortunately, the only way to get the
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computer running again would be to create a whole new Turing machine
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from scratch, but there\'s no *way* you can-\" He notices the look on
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your face, gives you a curious glance, shrugs, and goes back to sweeping
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the floor.
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You find the *Turing machine blueprints* (your puzzle input) on a tablet
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in a nearby pile of debris. Looking back up at the broken Turing machine
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above, you can start to identify its parts:
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- A *tape* which contains `0` repeated infinitely to the left and
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right.
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- A *cursor*, which can move left or right along the tape and read or
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write values at its current position.
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- A set of *states*, each containing rules about what to do based on
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the current value under the cursor.
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Each slot on the tape has two possible values: `0` (the starting value
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for all slots) and `1`. Based on whether the cursor is pointing at a `0`
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or a `1`, the current state says *what value to write* at the current
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position of the cursor, whether to *move the cursor* left or right one
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slot, and *which state to use next*.
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For example, suppose you found the following blueprint:
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Begin in state A.
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Perform a diagnostic checksum after 6 steps.
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In state A:
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If the current value is 0:
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- Write the value 1.
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- Move one slot to the right.
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- Continue with state B.
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If the current value is 1:
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- Write the value 0.
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- Move one slot to the left.
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- Continue with state B.
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In state B:
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If the current value is 0:
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- Write the value 1.
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- Move one slot to the left.
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- Continue with state A.
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If the current value is 1:
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- Write the value 1.
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- Move one slot to the right.
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- Continue with state A.
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Running it until the number of steps required to take the listed
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*diagnostic checksum* would result in the following tape configurations
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(with the *cursor* marked in square brackets):
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... 0 0 0 [0] 0 0 ... (before any steps; about to run state A)
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... 0 0 0 1 [0] 0 ... (after 1 step; about to run state B)
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... 0 0 0 [1] 1 0 ... (after 2 steps; about to run state A)
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... 0 0 [0] 0 1 0 ... (after 3 steps; about to run state B)
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... 0 [0] 1 0 1 0 ... (after 4 steps; about to run state A)
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... 0 1 [1] 0 1 0 ... (after 5 steps; about to run state B)
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... 0 1 1 [0] 1 0 ... (after 6 steps; about to run state A)
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The CPU can confirm that the Turing machine is working by taking a
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*diagnostic checksum* after a specific number of steps (given in the
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blueprint). Once the specified number of steps have been executed, the
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Turing machine should pause; once it does, count the number of times `1`
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appears on the tape. In the above example, the *diagnostic checksum* is
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*`3`*.
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Recreate the Turing machine and save the computer! *What is the
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diagnostic checksum* it produces once it\'s working again?
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To begin, [get your puzzle input](25/input).
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Answer:
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