Summarize the significance of the halting problem in the field of theoretical computer science.
In theory of computation, the halting problem is considered to be a decision problem, in which it is analyzed that whether a turing machine computation will ever terminate, when a set of finite input is provided. So, it basically helps in determining the program's lifecycle with the help of some description about the program and a set of finite input.
The inability to decide whether a problem (halting problem) will ever halt or not is a very old research result in the field Theory of Computation. But still it considered that on a finite state computer systems it is possible to determine the state of a problem. Therefore, if any undecidability proof given for the problem must be applicable for systems other than finite state machines.
The basic problem that needed to be evaluated is, whether a particular problem will eventually stop or not, here the concern is not that how long the program will execute in terms of time and not even concerned about the storage space that program occupies, but the concentration is to find and realize whether the given program will finally halt with a ...
The expert summarizes the significance of the halting problem in the field of theoretical computer science.