The computing power of Turing machine based on quantum logic (original) (raw)
Turing machines based on quantum logic can solve undecidableproblems. In this paper we will give recursion-theoreticalcharacterization of the computational power of this kind of quantumTuring machines. In detail, for the unsharp case, it is proved thatΣ<sup>0</sup><sub>1</sub>∪Π<sup>0</sup><sub>1</sub>⊆L<sup>T</sup><sub>d</sub>(ε,Σ)(L<sup>T</sup><sub>w</sub>(ε,Σ))⊆Π<sup>0</sup><sub>2</sub>when the truth value lattice is locally finite and the operation ∧is computable, whereL<sup>T</sup><sub>d</sub>(ε,Σ)(L<sup>T</sup><sub>w</sub>(ε,Σ))denotes theclass of quantum language accepted by these Turing machine indepth-first model (respectively, width-first model);for the sharp case, we can obtain similar results for usual orthomodular lattices.
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