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Miloslav Ciz 2023-11-26 21:32:39 +01:00
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turing_machine.md
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@ -4,6 +4,8 @@ Turing machine is a mathematical model of a [computer](computer.md) which works
The advantage of a Turing machine is that it's firstly very simple (it's basically a finite state automaton operating on a memory tape), so it can be mathematically grasped very easily, and secondly it is, unlike many other systems of computations, actually similar to real computers in principle, mainly by its sequential instruction execution and possession of an explicit memory tape it operates on (equivalent to [RAM](ram.md) in traditional computers). However note that a **pure Turing machine cannot exist in reality** because there can never exist a computer with infinite amount of memory which Turing machine possesses; computers that can physically exist are really equivalent to [finite state automata](finite_state_automaton.md), i.e. the "weakest" kind of systems of computation. However we can see our physical computers as [approximations](approximation.md) of a Turing machine that in most relevant cases behave the same, so we do tend to theoretically view computers as "Turing machines with limited memory".
In Turing machine data and program are separated (data is stored on the tape, program is represented by the control unit), i.e. it is closer to [Harvard architecture](harvard_architecture.md) than [von Neumann architecture](von_neumann_architecture.md).
**Is there anything computationally more powerful than a Turing machine?** Well, yes, but it's just kind of "mathematical fantasy". See e.g. [oracle machine](oracle_machine.md) which adds a special "oracle" device to a Turing machine to make it [magically](magic.md) solve undecidable problems.
## How It Works
@ -12,7 +14,7 @@ Turing machine has a few different versions (such as one with multiple memory ta
A Turing machine is composed of:
- **memory tape**: Memory composed of infinitely many cells (numbered 0, 1, 2, ...), each cell can hold exactly one symbol from some given alphabet (can be e.g. just symbols 0 and 1) OR the special *blank* symbol. At the beginning all memory cells contain the *blank* symbol.
- **memory tape**: Memory composed of infinitely many cells (numbered 0, 1, 2, ...), each cell can hold exactly one symbol from some given alphabet (can be e.g. just symbols 0 and 1) OR the special *blank* symbol. At the beginning all memory cells contain the *blank* symbol. Memory holds the [data](data.md) on which we perform computation.
- **read/write head**: Head that is positioned above a memory cell, can be moved to left or right. At the beginning the head is at memory cell 0.
- **control unit**: The program ([algorithm](algorithm.md)) that's "loaded" on the machine (the controls unit by itself is really a [finite state automaton](finite_state_automaton.md)). It is composed of:
- **a [set](set.md) of N (finitely many) states** {Q0, Q1, ... QN-1}: The machine is always in one of these states. One state is defined as starting (this is the state the machine is in at the beginning), one is the end state (the one which halts the machine when it is reached).