Introduction
About the lecture
Post's Correspondence Problem
Statement
Let $\alpha_1, \ldots, \alpha_n$ and $\beta_1, \ldots, \beta_n$ be sequences of words over a fixed alphabet. There exists a finite sequence $ a_1a_2 \ldots a_k$ , with $ a_i = 1, \ldots, n$ such that:
$\alpha_{a_1}\alpha_{a_2}\ldots \alpha_{a_k} = \beta_{a_1}\beta_{a_2}\ldots \beta_{a_k}$
Example
- Motivation:
- Simplifications:
- Limit the length of
- Header problem (highly decidable)
How to find “no” instances for PCP: https://webdocs.cs.ualberta.ca/~mmueller/ps/jea.pdf
Wang Tiling Problem
- Statement:
- Motivation:
- Simplifications:
- Limit the length of
Independent Set Problem
- Statement:
- Motivation:
- Simplifications:
- Limit the length of
Graph isomorphism Problem
- Statement:
- Motivation:
- Simplifications:
- Limit the length of