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$K\;\leq\;\{ \langle p,q\rangle \mid \exists y:\;(M_p(y){\downarrow} \,\wedge\, M_q(y){\downarrow}) \}$
Reduce $K$ to the set of pairs of natural numbers codifying programs halting
with a common input (roughly, the set of pairs of programs which stop with the
same common input), in order to prove that such set is undecidable (not
recursive).
Authors: Carles Creus, Guillem Godoy
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