Exercise 22:

{u,v,RΣ={a,b}    uRv}{u,v,RΣ3    uRvv}\{\langle u,v,R\rangle\mid\Sigma=\{a,b\}\;\wedge\;u\to_R^*v\}\quad\leq\quad\{\langle u,v,R\rangle \mid |\Sigma|\leq 3\;\wedge\;u\to_R^*vv\} (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,R\langle u,v,R\rangle where u,vu,v are words, RR is a word rewrite system, the used alphabet has at most 33 symbols, and uu reaches vvvv 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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