Paper used in furniture design. Watercolor paper has a long history of production and use. The thickness of paper is often measured by caliper, which is typically given in thousandths of an inch in the United States and in micrometers (µm) in the rest of the world. Paper may be between thick. Paper is often characterized by weight. In the United States, the weight assigned to a paper is the weight of a ream, 500 sheets, of varying "basic sizes", before the paper is cut into the size it is sold to end customers. For example, a ream of 20 lb,
Many-one reduction in: We say that a class C of languages (or a subset of the power set of the natural numbers) is "closed under many-one reducibility" if there exists no reduction from a language in C to a language outside C. If a class is closed under many-one reducibility, then many-one reduction can be used to show that a problem is in C by reducing a problem in C to it. Many-one reductions are valuable because most well-studied complexity classes are closed under some type of many-one reducibility, including P, NP, L, NL, co-NP, PSPACE, EXP, and many others. These classes