In the fair cake-cutting, two different computational models are used:A discrete model, in which the algorithm issues queries to the players and proceeds according to their replies;A continuous model, in which one or more knives move continuously over the cake under certain restrictions, until a player shouts stop.The continuous model is strictly stronger: there are problems that can be solved easily in the continuous model, but cannot be solved in finite time in the discrete model, e.g, envy-free cake-cutting with connected pieces.So I wonder what other problems, besides cake-cutting, can benefit from a moving knife or a similar continuous model? For example, is there a continuous variant of a Turing machine, that can easily solve problems that are unsolvable for a discrete Turing machine?
What can you do with a moving knife besides cutting a cake?
computability;turing machines;machine models