Testing can be automated, but it's highly unlikely that your automated testing is going to catch every problem.
We got involved in an emergency "replace this component" job at work recently. When the inevitable "how are we going to test this" questions started cropping up we did describe how we'd made half a million automated tests and that we had a reasonable understanding of the < 1% failure rate.
Testing is different from creation, though. In creating software, you make exclusive choices between options for how it will be made. But in testing, you can apply every testing strategy and they will complement each other. As one exhausts itself, mining out its favored part of bug space, the others become relatively better at finding the remaining bugs.
Oh, the actual project was an emergency hack where we accidentally reverse engineered what the component we were trying to replace, and then went on to outperform the original 100 fold. Very creative enterprise.
We got involved in an emergency "replace this component" job at work recently. When the inevitable "how are we going to test this" questions started cropping up we did describe how we'd made half a million automated tests and that we had a reasonable understanding of the < 1% failure rate.