Exercise 10:

{u,v,RΣ={a,b}    uRv}{u,v,RΣ2    uRv with an odd number of steps}\{\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 2\;\wedge\;u\to_R^*v\text{ with an odd number of steps}\} (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 22 symbols, and uu reaches vv using RR with an odd number of steps, 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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