Halting Problem

In Computability Theory, the halting problem is the problem of determining, from a description of an arbitrary computer program and an input, whether the program will finish running, or continue to run forever.

Alan Turing proved in 1936 that a general algorithm to solve the halting problem for all possible program–input pairs cannot exist.

title: Does an algorithm exist that can figure out if a program will halt for any input? 
No! WE can prove this by contradiction.
However, we can determine this for certain programs, by looking at [[Bounded Function|Bounding Function]].