80 lines
1.6 KiB
Perl
80 lines
1.6 KiB
Perl
◊h1{Turing machines}
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◊h2{Introduction}
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One of the motivators is exploring the limits of computation via the halting
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problem:
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halt :: function → bool
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The question is: does `function` always return? This is an undecidable problem.
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The Chomsky hierarchy:
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1. Regular expressions
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2. Simple programming languages
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3. Complex programming languages
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4. Turing equivalence
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◊h2{Computing by changing}
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Imperative model of computation: order of instructions matters, and generally
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destructive operations.
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Turing machine:
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* infinite tape composed of cells, initialisation is the blank symbol ('B')
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* head pointing to a cell on the tape
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* instructions: head movement, read, write
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Example machine: X_B
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two-cell tape:
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```
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BB
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^
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```
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rewrite first cell with X->B repeatedly: when we see a B, write an X. When we see an X, write a B.
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head has to move on every single instruction, only one step
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we'll move to the right
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cell 2: read B, see B, move left
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ex:
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BB
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^
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XB
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^
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XB
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^
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BB
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^
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Turing machines aren't imperatively organised; it uses a state table.
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state symbols:
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s_1...s_4
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(symbol, state) -> write, head move, next state
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B, s1 -> X, R, s2
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B, s2 -> B, L, s3
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X, s3 -> B, R, s4
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B, s4 -> B, L, s1
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a state table and four-line turing machine:
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X_B = {
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('B', 's1'): ('X', 'R', 's2'),
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('B', 's2'): ('B', 'L', 's3'),
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('X', 's3'): ('B', 'R', 's4'),
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('B', 's4'): ('B', 'L', 's1')
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}
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def simulate(instructions):
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tape, head, state = ['B', 'B'], 0, 's1'
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for _ in range(8):
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(tape[head], head_dir, state) = instructions[(tape[head], state)]
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head += 1 if head_dir == 'R' else -1
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simulate(X_B)
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