1. The halting problem is the problem of determining, from a description of an arbitrary computer program and an input, whether the program will finish running (i.e., halt) or _______________________.

2. Alan Turing proved in 1936 that a general algorithm to solve the halting problem for all possible program-input pairs cannot exist.

3. A key part of the proof was a mathematical definition of a computer and program, which became known as a _________________.

4. The halting problem is undecidable over Turing machines. It is one of the first examples of a ____________.

5. Read the excerpt below and decide whether the following statement is true or false: No f can exist that handles this case.

6. The problem is to determine, given a program and an input to the program, whether the program will ______________________________.

7. Analyse the program (pseudocode) below. This program will ________________________________.

8. The following program also does not halt.

9. Turing proved no algorithm exists that always correctly decides whether, for a given arbitrary program and input, the program halts when run with that input.

10. The essence of Turing's proof is that any such algorithm can be made to ______________________________.

11. Read the excerpt and problem below. Decide which answer is most accurate in response to the question.

12. The halting problem is theoretically decidable for linear bounded automata (LBAs) or deterministic machines with _______________.

13. A machine with finite memory has a finite number of states, and thus any deterministic program on it must eventually either halt or repeat a previous state

14. The halting problem is historically important because it was one of the first problems to be proved ____________.

15. The ____________ as shown below, represents the halting problem

16. The proof that the halting problem is not solvable is a proof by ________________.

17. Read the excerpt below and fill in the blanks.

18. The concepts raised by GĂ¶del's incompleteness theorems are very similar to those raised by the halting problem, and the proofs are quite similar

19. Fill in the blanks in the following excerpt.

20. The halting problem on usual computers is ___________. To see this, note that there are a finite number of bits in the memory, and thus a finite number of possible configurations the computer can be in.