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.

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

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



see also