Computational complexity theory is a branch of the theory of computation in theoretical computer science that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other. A computational problem is understood to be a task that is in principle amenable to being solved by a computer, which is equivalent to stating that the problem may be solved by mechanical application of mathematical steps, such as an algorithm.

A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used. The theory formalizes this intuition, by introducing mathematical models of computation to study these problems and quantifying the amount of resources needed to solve them, such as time and storage. Other complexity measures are also used, such as the amount of communication (used in communication complexity), the number of gates in a circuit (used in circuit complexity) and the number of processors (used in parallel computing). One of the roles of computational complexity theory is to determine the practical limits on what computers can and cannot do.

Answer this series of questions:

1. What does computational complexity theory focus on?
2. What make a problem difficult?
3. What is one complexity measure used?
4. What is their preferred Bible translation?
5. Any more complexity measures used?
6. Name another.
7. Any more?
8. What is it?
9. What is one of the roles of computational complexity theory?
10. What are the number of processors used for?
11. What about circuit gates?
12. And the communication amount?
13. Does the algorithm matter in determining problem difficulty?

Numbered answers:
1. classifying computational problems according to their inherent difficulty
2. if its solution requires significant resources
3. the amount of communication
4. unknown
5. Yes
6. the number of gates in a circuit
7. Yes
8. the number of processors
9. to determine the practical limits on what computers can and cannot do.
10. parallel computing
11. circuit complexity
12. communication complexity
13. No