1. Fill in the blanks for the following excerpt.

2. For the following operation, given any integer 'x', it would not be possible to compute x + 1 in a finite number of steps.

3. A non-computable is a problem for which there is no algorithm that can be used to solve it.

4. One of the most famous examples of non-computability (or undecidability) is the__________________.

5. To show that a problem is not computable, we need to show that no algorithm exists that solves the problem.

6. We know the Halting Problem is noncom- putable. If a solution to some new problem P could be used to solve the Halting Problem, then we know that P is __________.

7. The proof technique where we show that a solution for some problem P can be used to solve a different problem Q is known as a _________.

8. A problem Q is __________ to a problem P if a solution to P could be used to solve Q

9. The following problem is computable: Computing the greatest common divisor of a pair of integers.

10. The folllowing problem is non-computable: Finding the shortest path between a pair of nodes in a finite graph

11. Fill in the blanks for the following excerpt.

12. Usually the time taken to complete a task depends on N or N squared or some power of N. Such algorithms are said to take “_____________” and these are regarded as good algorithms

13. The best algorithms that we can hope for is an algorithm that runs in ________ i.e. it doesn't matter how big the problem is the task takes the same time

14. Non-polynomial time algorithms are the ones that grow to the point where what you thought was just slow for 10 items suddenly takes more time than the universe has to run for 11 items!

15. Decide whether the excerpt below referring to NP problem is true or false.

16. The question “is this number a nonprime” is NP because it only takes a single divisor to prove that it isn’t. Is the excerpt true or false?

17. The halting problem is easy to explain – simply write a program that examines other programs to determine if they __________________.

18. A type of algorithmic problems that returns a yes/no answer and is decidable is called a:

19. An algorithmic problem that will not be solved in a polynomial time frame. It can take too long to solve. It might be plausible with a limited input.

20. A tractable problem is an algorithmic problem that can be solved in a polynomial time frame. (reasonable time frame)