Final answer:
Turing machines with a double infinite tape have equivalent computational power to ordinary Turing machines, as they can simulate the same set of computable functions without offering improvements in memory storage or runtime efficiency.
Step-by-step explanation:
The equivalence established regarding Turing machines with a double infinite tape compared to ordinary Turing machines is that they have equivalent computational power, which is option D. A Turing machine with one tape that is infinite in both directions (also known as a double-ended infinite tape) can be simulated by a standard Turing machine with a single-sided infinite tape. This is because the movements and computations that can be performed on a double infinite tape can be mapped and simulated on a regular tape by effectively using a scheme to represent both directions.
Even though having a double infinite tape might seem like it would provide enhanced memory storage or faster runtime, in terms of Turing machine theory, it does not result in a machine that can solve problems that a standard Turing machine cannot solve. Both machines are equivalent in terms of the classes of problems they can compute, as determined by the Church-Turing thesis.