Public means API? AlphaGo is very specialized in solving Go game. Google, Amazon and IBM have services for various services like image recongition and speech recongition. Startups like Clarifi also exists in that space.
The closest to a generalized AI service would probably be Watson from IBM (but I don't have experiment with it sadly so I am not sure about the usage experience).
Public in the sense of non proprietary, in this case most likely universities.
My question was more : Google probably based its tools on existing tools, and those most likely come from universities (research paper, computer infrastructures, etc.). So what are those tools, where are they ?
The closest to a generalized AI service would probably be Watson from IBM (but I don't have experiment with it sadly so I am not sure about the usage experience).