To prove a program or normal thing(strings or languages) undecidable or decidable there are some technology. The technology is based on a very simple model of a computer called the Turing Machine. The Post Correspondence Problem is an undecidable problem that turns out to be a very helpful tool for proving problems in logic or in formal language theory to be undecidable.
What is undecidable?
The, specific, problem that cannot be solved using a computer are called undecidable. In computing there always exist some. That is a program and an input, whether the program will finish running or continue to run forever.
Suppose, we have step by step procedure(Algorithm) to solve a particular problem. We give the input(problem) and if that procedure can solve it, it gives the result true and if it not it give the result false. what if we give that procedure input(problem)which run forever that it take very long time(years) to get the result(TRUE or FALSE), then we can't make the decision out of it. This situation is undecidable.