X-Nico

4 unusual facts about Turing equivalence


Counter machine

However, the reader needs to be cautioned that, even though the μ operator is easily created by the base instruction set doesn't mean that an arbitrary partial recursive function can be easily created with a base model -- Turing equivalence and partial recursive functions imply an unbounded μ operator, one that can scurry to the ends of the register chain ad infinitum searching for its goal.

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Minsky shows that if two or more registers are available then the simpler INC, DEC etc. are adequate (but the Gödel number is still required to demonstrate Turing equivalence; also demonstrated in Elgot-Robinson 1964 ).

Turing equivalence

Turing completeness, having computational power equivalent to a universal Turing machine

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Turing degree equivalence (of sets), having the same level of unsolvability



see also