Home > Post correspondence problem

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.

1 Definition of the problem

The input of the problem consists of two finite lists:

and

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.

2 Example of an instance of the problem

Consider the following two lists:

A solution to this problem would be the sequence 1, 4, 3, 1 because

If the two lists had consisted of, for example, only and then there would have been no solution.

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