Problem reduction is a fundamental concept and methodological approach in computer science, artificial intelligence, and complexity theory. It involves transforming a given complex problem into one or more simpler sub-problems, or demonstrating its solvability through transformation into another known problem. This technique investigates how problems can be decomposed, mapped, or related to facilitate analysis, algorithm design, and classification based on computational difficulty. Its key characteristics include the definition of transformation rules between problem instances and the establishment of a relationship ensuring that a solution to the reduced problem(s) implies a solution to the original. The significance of problem reduction lies in its role as a powerful strategy for developing algorithms, navigating search spaces in artificial intelligence, and establishing hierarchies within computational complexity theory, particularly in defining classes like NP-completeness.