Can all types of computational problems (search, counting, optimization...) be modeled as (sets of) decision problems? Rephrased: For every type of computational problem is there a set of decision problems that if you solve those problems you get the result of the original problem?
colloquially: can all types of questions you can ask a string be answered by (a series of) results from YES NO questions? So the game is: you are given a question about a string, you are allowed to ask the string only YES NO questions. The string responds with answers to your YES NO questions that are computable. Can you compose all the answers you receive to narrow in on THE SINGLE answer to the original question (not a spread of answers / not some result but with a probability attached)?
Decision problems can be modeled as word to language membership. On the surface, this only models the functions that go from f:{0,1} * -->1 not all the other types of functions. Some g: {0,1} * -->{0,1} * for example. But I have a feeling the answer could be yes...