Yes but it's (kind of?) a definition as you asked for.

At this point, I am unaware of a better definition. I know the Chinese Room argument (and I disagree with it), but I'm not aware whether the proponents of that argument have a better definition of understanding other than "well, the Turing Test isn't enough"...

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PS: Interestingly the issue of compression is highly relevant regarding the Chinese Room argument -- the essential element in the Chinese Room argument is that the information is not compressed...