Question

For every decision problem there is a polynomial time algorithm that solves it?

1) False
2) True

Answer 1

The statement is 1) false because there are decision problems that are proven to be unsolvable by any polynomial time algorithm.

Step-by-step explanation:

In computational complexity theory, there is a class of problems known as decision problems. These are problems that can be answered with a simple yes or no. The question asks whether every decision problem has a polynomial time algorithm that solves it. The correct answer is False. This is because there are decision problems that are proven to be unsolvable by any polynomial time algorithm.

One example of an unsolvable decision problem is the Halting Problem, which asks whether a given program will halt or run forever. Alan Turing proved in 1936 that there is no algorithm that can solve the Halting Problem for all programs. There are other decision problems that are similarly proven to be unsolvable.

While there are many decision problems for which we have efficient polynomial time algorithms, it is not true that every decision problem falls into this category. Therefore, the statement is false.