I feel you’d be unlikely to see “denomination”, on what I assume to be a public-facing machine, as many might not understand it.
“Value” you may see, but I feel it would more likely just be something like:
The machine accepts all coins.
I also feel that there’d be a possibility that you would still see every denomination listed, even if it’s all of them, just to be totally clear and explicit.
In the Computer Science context you mentioned, I'd probably specify the currency. You may hear something like:
The machine accepts coins of any denomination of the United States dollar.
I'll be honest though, this is the kind of sentence that even many native speakers would struggle to figure out how to phrase correctly (in a way that is erudite but also easy to read), even Computer Scientists. If they know the word "denomination", they'll probably try to use it, and figure out the best way of phrasing it.