Counterfactual Effect, the Halting Problem, and the Busy Beaver Function
Cristian S. Calude, Michael J. Dinneen, Karl Svozil · 1999
Using the counterfactual effect, we demonstrate that with better than 50% chance we can determine whether an arbitrary universal Turing machine will halt on an arbitrarily given program. As an application we indicate a probabilistic method for computing the busy beaver function--a classical uncomputable function. These results suggest a possibility of going beyond the Turing barrier.