The canonical example for me(which was ironically is in Half-Life) is that the AI for the grunts is surprisingly simple. If you throw a grenade they were scripted to shout "grenade" and navigate to the nearest nav node.
Tons of people thought there was really complex AI behind that behavior but it was just a couple of really well telegraphed "if()" checks.
I guess if you are able to formulate the problem as a state machine, you could use something like bounded model checking to ensure it doesn't blow up, but the problems there are twofold: Firstly, that's way too complicated and brittle for a game codebase, and secondly your average game developer probably doesn't even know what it is to begin with.
This is probably just me not really understanding the domain, but this sounds like a version of the halting problem?
Even if it’s not, isn’t that just an extra layer doing what the collision engine is meant to do in the first place? And if you can monitor a system to ensure correctness, couldn’t you use a similar mechanism to make the original system correct to begin with? And if you can’t do that, how can you expect to make the supervisory layer correct?
For that reason there should be a "user level" interpretation of the physics engine results, looking ahead in time and correcting.
“Let’s monitor in real time for whether any possible combination of inputs could produce a technically valid but undesirable state” doesn’t sound any less complicated or more effective than finding bugs and fixing them.
The Destiny version doesn’t require understanding the bug, only recognizing after the fact that the player has, say, clipped out of bounds. Doesn’t matter how you got there. That sounds like a decent compromise for a pvp game where preventing exploits is very important.
But being able to extrapolate that the current state will lead to a bad state implies that you already understand the bug and could, you know, fix it.
Yes, you could have for example energy limiters and total momentum checks in your algorithms. Energy can not be added in a collision. In a collision between two finite mass objects, total momentum is preserved (you can't use this with collisions with the ground). Maybe games already do this?
You could also just fudge the equations to avoid singularities, like always add +1 to the divider. This could probably cause other problems though.