===== 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 $math[a_1a_2 \ldots a_k], with $math[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