Exercise 20:

{u,v,RΣ={a,b}    uRv}{u,v,w,RΣ3    uRvRw    uvw}\{\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 3\;\wedge\;u\to_R^*v\to_R^*w\;\wedge\;u\neq v\neq 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 33 symbols, uu reaches vv using RR, vv reaches ww using RR, uu is different from vv, and vv is different from ww, 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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