Halting Problem: Given an input Turing machine $M$ (in some encoded form) and a word $w,$ we have to decide if $M$ halts on $w.$
In programming terms, this is equivalent to saying if a program will finish running on a given input.
Now, answering this problem is straightforward if the answer is "yes" -- we just have to run the TM on the given input and say "yes" when it halts. But answering "no" is not straight forwards as the TM may go to an infinite loop from which we are no sure if it'll eventually come out or not.
Thus Halting problem albeit semi-decidable is undecidable. It's complement is not even semi-decidable.
