> Yes it is, it's Turing-completeness.

While this may be a sensible interpretation, and I am willing to believe it's used in that interpretation in some fields, I have a hard time actually finding a definition of that form.

I also have a problem with using it in this way: In circuits the size of the circuit limits your input size. But given a maximum size of the input, and no size limitations on the circuit, you can construct a circuit that produces the same result as a turing machine that halts. So you can compute whatever you want (i.e. arbitrary) but you are limited by the size of your current circuit.

(Completely unhelpful but always fun to look at for words: https://books.google.com/ngrams/graph?content=arbitrary+comp... )