We know all optimisation problems can be converted to decision problems. Is that true for search problems, counting problems and function problems as well? Description of the types of problems is given here: Computational problem.
Edit: So, the comments suggest that I state more precisely what I mean. I'm not entirely sure how to do that, so I'll tell you where I'm coming from. I understand that a Turing machine can solve only decision problems (It can accept or reject a string). I am wondering if a Turing machine can solve all kinds of problems - which is why I ask, can all those types of problems be expressed as decision problems?
A better way to put it would probably be, can all those types of problems be expressed in a way that they might be solved by a Turing machine?