Comment by WorldMaker
2 hours ago
It's my view of the Halting Problem that we've known for a surprisingly long time that eliminating all software bugs is mathematically impossible and should stop letting perfect get in the way of the good.
Especially with the more recent relative of the Halting Problem combined with the Church-Turing Theorem that found mathematical proof of a "0-day" sandbox escape in the Universal Turing Machine itself.
We have always lived in a house of glass. LLM agents automating trebuchets for rock throwing certainly seems like a bad idea to me and "let's simply eliminate all software vulnerabilities" an interesting bit of ostrich work (stick your head in the sand and hope it all gets better).
This has little to do with the halting problem, because we can choose to not deploy programs (or subroutines) that we want to be terminating but can’t prove that they are terminating. And that goes for any undecidable problem. There is no application where we want the program to have a certain property where we would be forced to deploy a program where we can’t prove the property due to computational theory reasons.
No, the real issue is that for the most we don’t want to put the necessary effort into proving the relevant properties, because it’s costly and time-consuming, and we think we can live with the risk. The issue is not some theoretical inability to do so.
We absolutely have pragmatic compromises and shortcuts for dealing with termination problems, but that doesn't mean we've solved the Halting Problem, it means we've adapted to coexistence with it. (And maybe we've coexisted with the Problem for long enough it feels like most of those adaptations are sufficient day to day, which makes it all the harder to appreciate the bugs that are always there we just mitigate enough to worry about them less.)
Potentially Infinite Loops are a great power. We've learned in most programming languages the "Uncle Ben lesson" that with such great power, comes great responsibility. In most programming languages we don't want to remove the ability to infinitely loop, because we might need that power, we work on ways to limit that responsibility (loop guards and timeouts and cancellations and teardowns). But it will likely always be possible to see some code spin in a loop we can't tell is accidentally infinite or just a loop with a lot more work than we expected. The infinite spin wait will always be a risk in our code.
I think it has a lot to do with the Halting Problem.
An infinite loop doesn’t mean that you can’t prove whatever property you want to prove about your program, if you’ve designed it for that. The limitations coming from undecidability don’t really affect our everyday applications. Unless your application is exactly to determine whether another arbitrary program will halt, that is. But that’s not what the vast majority of software whose bugs we might be concerned about is about.
“We can’t write bug-free software due to the halting problem anyway” is an incorrect argument.
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