Question

I’m wondering what would be a ‘concise’ definition of computable? I ask because I have become confused over what is computable or not.

Is something only computable if it comes to a halt? For instance

function foo(){
 while(true);
}

Is not computable, simply because it never comes to a halt? Or am I confusing the definition of computable with the halting problem?

Thanks

Answer 1

Something is formally computable if, given the capabilities of a certain (often purely theoretical) computer, you can show that there is an algorithm which will solve that problem in finite time.

So computability is a property of the computer and the problem, not of a piece of code.

Two of the interesting results of studying computability:

• Certain classes of computers are more limited than others in regard to what is computable on them, but even some very simple models (such as Turing machines) can compute everything we know how to compute.
• Some problems can be proven to be non-computable or undecidable. The halting problem is one such problem.