Not 99% of programs. And even if they could, they never are.
Besides AI is a program in the same sense. Fix the seed/temperature, and you can verify it to perform according to its specifications. It's just that its specificactions include returning answers based on a weight model.
You misunderstand. Incomplete specification is still useful. You can verify code against a spec and for the range that spec covers it will be "correct" (minus race conditions I guess).
You can't verify anything with AI. Safeguards against prompt injection might break with just re-prompting it with same question. Or break when AI vendor updates their model.