The Halting Function

The Halting Function

    With the introduction of the halting function, it brings up an interesting concept. The way I see it is we create a function which has two outputs and then create the body of the function which emulates these two functions. So in essence the definition of the outputs is what's making such a function be impossible to implement. Furthermore when we use reduction to prove other functions as also being impossible to implement, using the halting functions definition simply allows us to make the second function meet its description as long as we somehow implement a piece of code where the function can either halt or not halt. As another student Ji stated on his blogger, even with Turing complete programming languages some programs are impossible to write. I recall reading about how in practice, some situations may be similar to the halting function in the sense that what they're trying to solve is not computable. And so the program designed would be aimed at optimizing a solution and then finding a better one. This would be run over and over so in essence its finding a better solution compared to the current solution. If a solution to the halting function were created, I'm not so sure as to the practicality of it save for those cases which model the halting problem. 

    I'm interested in further such examples of these theoretical computer science cases and am looking forward to learning more about them. In regards to the halting problem I don't see a solution arising unless the program can determine whether or not it will run infinitely. This would require quite a lot of intuition on the programs part. We've probably not gotten to that point yet in machine learning and artificial intelligence as we still haven't solved this problem yet. On that note though and with figures such as Elon Musk and Stephen Hawking warning us about advances in machine learning and artificial intelligence I'd probably lean towards not getting to that point.