Introduction to Reductions and Complexity Theory
In computability theory and computational complexity theory, a reduction is an algorithm for transforming one problem into another problem. A sufficiently efficient reduction from one problem to another may be used to show that the second problem is at least as difficult as the first.
Understanding Time Complexity
- Is O M * N linear?
- What does O1 mean?
- What is quadratic time?
To sum up: O(mn) is generally called linear for things like matrix multiplication because it’s linear in the size of the input, but it’s generally called quadratic for things like string matching because of the smaller input.
Exploring Complexity Classes
- Is chess a NP?
- Is P NP solvable?
For two-player games, one encounters a similar phenomenon at a higher level of complexity. For this reason, games like chess cannot themselves be NP-complete, as they only have a finite (albeit unthinkably large) number of possible positions.
This subset is defined as P. P is the set of all decision problems that are efficiently solvable. P is a subset of NP. P is the set of all decision problems that are efficiently solvable and is a subset of NP. Basic Arithmetic is solvable in Polynomial-time and belongs to P.