No, tests are not specification, they are examples, specifically on the form "do this, and this happens".
Imagining a specification out of this is like solving those problems of "what is the next number on this sequence: 1 18 31". It's simply can not be done, you can guess something, but you will never know if it's the real answer.
That _can_ be examples but I prefer to write them as specs. I mean, there are entire libraries centred around writing tests as specs. Just because you don't do it that way or buy into the idea doesn't mean it's not possible or valuable.
Specs are complete. If you create real world software with complete tests, I will really want to read your Turing Award receiving discourse. It should be great.
Imagining a specification out of this is like solving those problems of "what is the next number on this sequence: 1 18 31". It's simply can not be done, you can guess something, but you will never know if it's the real answer.