Tests are there to prove everything you thought of works correctly. They do nothing to find things you didn't think of. However with effort ($$$) you can become very creative in thinking about failure cases that you then test.
If you want to find problems you didn't think of formal proofs are the only think I have heard of. However formal proofs only work if you can think of the right constraints (I forget the correct term) which isn't easy.
Note that the two are not substitutes for each other. While there is overlap there are classes of errors that one along will not catch. For most projects though it is more cost effective to live with some bugs for a long time than to spend enough money on either of the above to find it ahead of time. Different projects have different needs (games vs medical devices...)
If you want to find problems you didn't think of formal proofs are the only think I have heard of. However formal proofs only work if you can think of the right constraints (I forget the correct term) which isn't easy.
Note that the two are not substitutes for each other. While there is overlap there are classes of errors that one along will not catch. For most projects though it is more cost effective to live with some bugs for a long time than to spend enough money on either of the above to find it ahead of time. Different projects have different needs (games vs medical devices...)