Unfortunately, tests can never be a complete specification unless the system is simple enough to have a finite set of possible inputs.

For all real-world software, a test suite tests a number of points in the space of possible inputs and we hope that those points generalize to pinning down the overall behavior of the implementation.

But there's no guarantee of that generalization. An implementation that fails a test is guaranteed to not implement the spec, but an implementation that passes all of the tests is not guaranteed to implement it.

> Unfortunately, tests can never be a complete specification

They are for the human, which is the intended recipient.

Given infinite time the machine would also be able to validate against the complete specification, but, of course, we normally cut things short because we want to release the software in a reasonable amount of time. But, as before, that this ability exists at all is merely a secondary benefit.