Exercise 18:

{u,v,RΣ={a,b}    uRv}{u,v,w,RΣ2    uRvRw}\{\langle u,v,R\rangle\mid\Sigma=\{a,b\}\;\wedge\;u\to_R^*v\}\quad\leq\quad\{\langle u,v,w,R\rangle \mid |\Sigma|\leq 2\;\wedge\;u\to_R^*v\to_R^*w\} (morphism not allowed in the reduction)
Reduce the word reachability problem restricted to the alphabet {a,b}\{a,b\} to the set of tuples u,v,w,R\langle u,v,w,R\rangle where u,v,wu,v,w are words, RR is a word rewrite system, the used alphabet has at most 22 symbols, uu reaches vv using RR, and vv reaches ww using RR, in order to prove that such set is undecidable (not recursive).

The use of morphism is not allowed in the description of this reduction.
Authors: Guillem Godoy / Documentation:
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