Two cyborgs walk into your home, both claiming to be oracles for the graph 3-col

Question

Two cyborgs walk into your home, both claiming to be oracles for the graph 3-colorability decision problem. They both always give a yes/no answer in constant time for any instance, and are each self-consistent (i.e. each always gives the same answer for the same instance). However, one is a true oracle and the other is a shameless impostor, and you have a large instance of 3-colorability upon which they disagree. Prove whether it is possible to expose the impostor within time polynomial in the size of that instance

Explanation / Answer

Two cyborgs walk into your home, both claiming to be oracles for the graph 3-colorability decision problem. They both always give a yes/no answer in constant time for any instance, and are each self-consistent (i.e. each always gives the same answer for the same instance). However, one is a true oracle and the other is a shameless impostor, and you have a large instance of 3-colorability upon which they disagree. Prove whether it is possible to expose the impostor within time polynomial in the size of that instance

Solution:

Consider the x contains {0,1},y contains yes/no answer .

To identify and verify the x as input and y as output it contains yes/no answer and satisfies proper method in plolynomial time.

Thus the graph 3-colorability decision problem not solve with in polynomial time.

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