Exercise 15:

{u,v,RΣ={a,b}    uRv}{u,v,RΣ3    uR+v}\{\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^+v\} (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 vv using RR with at least one step, 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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