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:

$\alpha_{a_1}\alpha_{a_2}\ldots \alpha_{a_k} = \beta_{a_1}\beta_{a_2}\ldots \beta_{a_k}$

• 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

• Statement:
• Motivation:
• Simplifications:
  • Limit the length of

• Statement:
• Motivation:
• Simplifications:
  • Limit the length of

• Statement:
• Motivation:
• Simplifications:
  • Limit the length of