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| ==== About the lecture ==== | ==== About the lecture ==== | ||
| - | ==== Post's Correspondence Problem ==== | + | ===== 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 ==== | ||
| + | |||
| - | * Statement: | ||
| * Motivation: | * Motivation: | ||
| * Simplifications: | * Simplifications: | ||
| * Limit the length of | * 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 ==== | ==== Wang Tiling Problem ==== | ||