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Turing completness is being typically proved via reduction to already proved Turing-complete machine.

Can the same be obtained by showing, that the machine in question is capable of generating arbitrary output – if proper input is given?

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What is "arbitrary output" supposed to mean? – Raphael Nov 1 '12 at 14:18
agree question in current form is too vague or not well defined – vzn Nov 1 '12 at 16:58
up vote 4 down vote accepted

Turing-completeness means that the machine model in question can compute everything that is computable. That means that for every computable function $f$, there is a corresponding program for your model which behaves "like" $f$, where I put the quotes since the input and output may look differently.

Showing that the machine can generate arbitrary output is hardly enough - consider the machine model which executes only one program, copying its input to its output.

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Thanks Yuval, i was looking for this answer for a while => I have this model of computation (a Celluar Automaton) and by somehow it can generate arbitrary output (unbounded input => output), is it possible to provide some sources or specific topic to prove turing completeness by using arbitrary output ? – ABD Jan 10 at 0:30

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