How a TM can represent any algorithm?

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)?

Don't forget that the final content of the tape can be treated like the output of the algorithm that the TM computes; in other words, a TM is able to compute a function: there is no "reject state" but only an "accept state" and the function result is the content of the tape at the end of the computation.

But if you want to learn more on the relation between decision problems and function problems , (quickly) read the Decision Problem - Equivalence with functions problems entry on Wikipedia, and then search some lectures online on the subject.

StackExchange Computer Science Q#12781, answer score: 6