46 lines
1.4 KiB
Markdown
46 lines
1.4 KiB
Markdown
---
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tags:
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- theory-of-computation
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- Turing
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---
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# Turing Machines
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## What is a Turing Machine?
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Turing Machine is a machine that contains mutable state, executes sequences of
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simple instructions that read and write that state, and can pick different
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execution paths depending on the state (via conditional branch instructions.)
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This is a general expression, it is typically expanded as follows.
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The machine consists of an infinitely long tape, that has been divided up into
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cells. Each cell can contain either a 1, a 0 or an empty space. Above one cell
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of the tape is a head, which can either move left or right, and can read the
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symbols written in the cells. The head is also capable of erasing symbols and
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writing new symbols into the cells.
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The direction that the head moves, which values it erases, and which values it
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writes in, are dependent on a set of instructions provided to the machine.
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Different sets of instructions can be divided into **states.** States are like
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sub-routines and can themselves feature as part of instructions.
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For example:
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### State 2
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- If 0 then erase
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- Write 1 then move right
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- Go to state 5
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### State 5
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- If 1, then erase
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- Write 0 then move left
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- Go to state _n_
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Alan Turing proved that **any problem that is computable** can be computed by a
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Turing Machine using this simple system.
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