We know
if we have:
we can show (T=t= Turin Redu.)
but i have no idea why this relation be correct? any idea?
2026-03-26 02:25:24.1774491924
Turing & Computability & Computation
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Just prove that (for all $x$)
$$(2x+1)\in (A\oplus B)\oplus C \Longleftrightarrow (4x+3)\in A \oplus (B\oplus C)$$ $$(4x+2)\in (A\oplus B)\oplus C \Longleftrightarrow (4x+1)\in A \oplus (B\oplus C)$$ $$(4x)\in (A\oplus B)\oplus C \Longleftrightarrow (2x)\in A \oplus (B\oplus C)$$
Hence, (see 1-reduction) $$(A\oplus B)\oplus C \equiv_1 A \oplus (B\oplus C)$$
that implies Turing equivalence.