The solution to the halting problem is to stop building universal/Turing-complete machines.
Edit: since this was downvoted, I will elaborate. The halting problem only applies to arbitrary programs on Turing-complete systems. It is possible to create useful systems that are not Turing complete. As a baseline example, it is easy to tell that the following Ruby program halts:
exit
Problems arise when one allows unbounded loops and unbounded recursion. If all loops and all recursions are provably finite, then a program can be proven to exit. All sorts of useful things can be done with systems composed of small, provably terminating programs. And it turns out, the vast majority (if not all) of the things relevant to securing a computer system can be implemented in formally provable ways.
Edit: since this was downvoted, I will elaborate. The halting problem only applies to arbitrary programs on Turing-complete systems. It is possible to create useful systems that are not Turing complete. As a baseline example, it is easy to tell that the following Ruby program halts:
Problems arise when one allows unbounded loops and unbounded recursion. If all loops and all recursions are provably finite, then a program can be proven to exit. All sorts of useful things can be done with systems composed of small, provably terminating programs. And it turns out, the vast majority (if not all) of the things relevant to securing a computer system can be implemented in formally provable ways.