Can a program can do exactly some given task?

Is there any way to be sure that a given program will do exactly a specific task?
Let's say I want to make a round-robin scheduler. Is there some way that I can be sure that certain program I've written will do exactly that?

What you're talking about is Formal Verification:
http://en.wikipedia.org/wiki/Formal_verification

It's a royal pain in the ass to do, only worth doing when it's truly _critical_ something is correct (NASA for example)