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 problem is easy to solve. The many-one reduction is more effective at separating problems into distinct complexity classes. However, the increased restrictions on many-one reductions make them more difficult to find. Many-one reductions were first used by Emil Post in a paper published in 1944. Later Norman Shapiro used the same concept in 1956 under the name "strong reducibility". Suppose "A" and "B" are formal languages over the alphabets Σ and Γ, respectively. A many-one reduction from "A" to "B" is a total computable function "f" : Σ → Γ that has the property that each word "w" is in