Post correspondence problem Guide, Meaning , Facts, Information and Description
The Post correspondence problem is an undecidable decision problem that was introduced by Emil Post. Because it is simpler than the Halting problem and the Entscheidungsproblem it is often used in proofs of undecidability.Informally the problem can be described as follows. Given a dictionary that contains pairs of phrases, i.e., a list of words, that mean the same, decide if there is a sentence that means the same in both languages.
The input of the problem consists of two finite lists:
Consider the following two lists:
Definition of the problem
of words over some alphabet Σ with at least two symbols. A solution to this problem is a sequence of indexes , such that
The decision problem then is to decide whether such a solution exists or not.Example of an instance of the problem
A solution to this problem would be the sequence 1, 4, 3, 1 because
A convenient way to view an instance of a Post correspondence problem is as a collection of blocks of the form
Thus the above example is viewed as
|
|
, |
|
, |
|
, |
|
||||||||
A solution corresponds to some way of laying blocks next to each other so that the string in the top cells corresponds to the string in the bottom cells. Thus the solution of the above example corresponds to
|
|
, |
|
, |
|
, |
|
||||||||
This is an Article on Post correspondence problem. Page Contains Information, Facts Details or Explanation Guide About Post correspondence problem