A perfect predictor is an agent which can predict the behaviour of an agent or the outcome of an event with perfect accuracy. It is often given the name Omega, but Omega might also be an almost perfect predictor.
One challenge with perfect predictors is that it might be unclear what Omega is predicting. Take for example Parfit's Hitchhiker. In this problem, you are trapped dying in a desert and a passing driver will only pick you up if you promise to pay them $100 once you are in town. If the driver is a perfect predictor, then someone who always defects will never end up in town, so it is unclear what exactly they are predicting, since the situation is contradictory and the Principle of Explosion means that you can prove anything.
Counterfactuals for Perfect Predictors suggests that even if we can't predict what an agent would do in an inconsistent or conditionally consistent situation, we can predict how it would respond if given input representing an inconsistent situation (we can represent this response as an output). And indeed Updateless Decision Theory uses input-output maps so it doesn't run into this issue....