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    $\begingroup$ I think OP mixes up Turing machine and Turing complete. What he's actually looking for is the definition of a Turing machine; your last sentence is the answer. en.wikipedia.org/wiki/Turing_machine would help. $\endgroup$ Commented Mar 13, 2017 at 14:38
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    $\begingroup$ So what can a Turing machine do? As in, if I wanted to prove that something can emulate a Turing machine, what minimal set of behaviours must I be able to demonstrate that my machine can do too? $\endgroup$ Commented Mar 14, 2017 at 23:06
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    $\begingroup$ Never mind - I worked out that it is sufficient to demonstrate that a language can mimic the way a Turing machine operates in order to prove that it is Turing-complete. $\endgroup$ Commented Mar 14, 2017 at 23:14