What's the program in the Chinese Room?

It's really big and complicated!  That's my main takeaway from the Dennett writing on the Searle thought experiment (in Intuition Pumps and other books).

Here's the description of the scenario from Wikipedia:

It supposes that there is a program that gives a computer the ability to carry on an intelligent conversation in written Chinese. If the program is given to someone who speaks only English to execute the instructions of the program by hand, then in theory, the English speaker would also be able to carry on a conversation in written Chinese. However, the English speaker would not be able to understand the conversation. Similarly, Searle concludes, a computer executing the program would not understand the conversation either.

So - what might this program consist of?  Obviously there is no simple algorithm for taking in a string of Chinese characters one by one, and sending out a meaningful response character by character.  It would need all sorts of features, such as memory of the current conversation (to provide context to any given input), ability to distinguish questions from comments from opinions, and so much more.  Of course any such program could never be carried out in a step by step manual way by a person, unless you are willing to wait days if not months or years for responses!

If we simply assume that such a program exists and works as described, then it does seem to me that the outsider interacting with the room would grant a level of understanding to it.  The Watson program that can play Jeopardy seems to be getting relatively close to this level of sophistication, although it was built for the Answer/Question format only.