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turing_machine.md

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 # Turing Machine
 
-Turing machine is a mathematical model of a [computer](computer.md) which works in a quite simple way but has nevertheless the full computational power that's possible to be achieved. Turing machine is one of the most important tools of theoretical [computer science](compsci.md) as it presents a basic [model of computation](model_of_computation.md) (i.e. a mathematical system capable of performing general mathematical calculations) for studying computers and [algorithms](algorithm.md) -- in fact it stood at the beginning of theoretical computer science when [Alan Turing](alan_turing.md) invented it in 1936 and used it to mathematically [prove](proof.md) essential things about computers; for example that their computational power is inevitably limited (see [computability](computability.md)) -- he showed that even though Turing machine has the full computational power we can hope for, there exist problems it is incapable of solving (and so will be any other computer equivalent to Turing machine, even human [brain](brain.md)). Since then many other so called **[Turing complete](turing_completeness.md)** systems (systems with the exact same computational power as a Turing machine) have been invented and discovered, such as [lambda calculus](lambda_calculus.md) or [Petri nets](petri_net.md), however Turing machine still remains not just relevant, but probably of greatest importance, not only historically, but also because it is similar to physical computers in the way it works.
+Turing machine is a [mathematical](math.md) [model](model.md) of a [computer](computer.md) which works in a quite simple way but has nevertheless the full computational power that's possible to be achieved. Turing machine is one of the most important tools of theoretical [computer science](compsci.md) as it presents a basic [model of computation](model_of_computation.md) (i.e. a mathematical system capable of performing general mathematical calculations) for studying computers and [algorithms](algorithm.md) -- in fact it stood at the beginning of theoretical computer science when [Alan Turing](alan_turing.md) invented it in 1936 and used it to mathematically [prove](proof.md) essential things about computers; for example that their computational power is inevitably limited (see [computability](computability.md)) -- he showed that even though Turing machine has the full computational power we can hope for, there exist problems it is incapable of solving (and so will be any other computer equivalent to Turing machine, even human [brain](brain.md)). Since then many other so called **[Turing complete](turing_completeness.md)** systems (systems with the exact same computational power as a Turing machine) have been invented and discovered, such as [lambda calculus](lambda_calculus.md) or [Petri nets](petri_net.md), however Turing machine still remains not just relevant, but probably of greatest importance, not only historically, but also because it is similar to physical computers in the way it 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".
+The advantage of a Turing machine is that it's firstly very [simple](minimalism.md) (it's basically a finite state automaton operating on a [memory](memory.md) 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".
 
 { Although purely hypothetically we could entertain an idea of a computer that's capable of manufacturing itself a new tape cell whenever one is needed, which could then have something like unbounded memory tape, but still it would be limited at least by the amount of matter in observable universe. ~drummyfish }