Interactive Undecidable Problems

Explore and visualize famous undecidable problems in computer science

Post Correspondence Problem

The Post Correspondence Problem (PCP) asks whether, given two lists of strings X and Y, there exists a sequence of indices such that concatenating the strings from X in that order equals concatenating the strings from Y in the same order.

Undecidability:

PCP is undecidable for alphabets with at least two symbols. This means there is no algorithm that can determine for any arbitrary PCP instance whether a solution exists.

Example 1: PCP with a Solution

This PCP instance has a solution with the sequence (3, 2, 3, 1).

List X:

  • x₍1₎ = ab
  • x₍2₎ = a
  • x₍3₎ = baa

List Y:

  • y₍1₎ = aba
  • y₍2₎ = aa
  • y₍3₎ = b