The Post Correspondence Problem (PCP), introduced by Emil Post in 1946, is an undecidable decision problem. The PCP problem over an alphabet ∑ is stated as follows −
Given the following two lists, M and N of non-empty strings over ∑ −
M = (x1, x2, x3,………, xn)
N = (y1, y2, y3,………, yn)
We can say that there is a Post Correspondence Solution, if for some i1,i2,………… ik, where 1 ≤ ij ≤ n, the condition xi1 …….xik = yi1 …….yik satisfies.
Find whether the lists
M = (abb, aa, aaa) and N = (bba, aaa, aa)
have a Post Correspondence Solution?
x2x1x3 = ‘aaabbaaa’
and y2y1y3 = ‘aaabbaaa’
We can see that
x2x1x3 = y2y1y3
Hence, the solution is i = 2, j = 1, and k = 3.
Find whether the lists M = (ab, bab, bbaaa) and N = (a, ba, bab) have a Post Correspondence Solution?
In this case, there is no solution because −
| x2x1x3 | ≠ | y2y1y3 | (Lengths are not same)
Hence, it can be said that this Post Correspondence Problem is undecidable.