As I remember:
- A decision problem is a problem that has the answer yes or no.
- An algorithm (in the context of automata theory) answers yes or no; it halts on all inputs, accepted or not.
- A TM represents an algorithm. The TM accepts an input string and executes with that input. If the machine ends up in an accept state, the answer is yes, otherwise no.
How does a yes/no problem relate to general algorithms we are doing that have more than yes/no problems? Or is that every problem can be thought as a yes/no problem, i.e. is this a function f produce 5 (or whatever input) with input 2 (or whatever output)?