Question

What extra capabilities does a Turing reduction have compared to a polynomial-time mapping reduction? It can run for longer than polynomial time. In showing A is Turing reducible to B, the decider for A can call the decider for B and output the opposite answer. The reduction may not halt. In showing A is Turing reducible to B, the decider for A can call the decider for B more than once.

Answer 1

A Turing reduction has extra capabilities compared to a polynomial-time mapping reduction. It can run for longer than polynomial time, invert the decision of B, continue indefinitely, and allow multiple iterations.

Step-by-step explanation:

A Turing reduction has several extra capabilities compared to a polynomial-time mapping reduction:

1. It can run for longer than polynomial time, meaning it can take more time to compute solutions.
2. In a Turing reduction, the decider for A can call the decider for B and output the opposite answer, giving the ability to invert the decision of B.
3. The reduction may not halt, which means the reduction process may continue indefinitely without reaching a conclusion.
4. In a Turing reduction, the decider for A can call the decider for B more than once, allowing multiple iterations of the reduction process.