Reduction

Reduction, reduced, or reduce may refer to:

Science

Chemistry

Anatomical terms of motion

Motion, the process of movement, is described using specific anatomical terms. Motion includes movement of organs, joints, limbs, and specific sections of the body. The terminology used describes this motion according to its direction relative to the anatomical position of the joints. Anatomists use a unified set of terms to describe most of the movements, although other, more specialized terms are necessary for describing the uniqueness of the movements such as those of the hands, feet, and eyes.

In general, motion is classified according to the anatomical plane it occurs in. Flexion and extension are examples of angular motions, in which two axes of a joint are brought closer together or moved further apart. Rotational motion may occur at other joints, for example the shoulder, and are described as internal or external. Other terms, such as elevation and depression, refer to movement above or below the horizontal plane. Many anatomical terms derive from Latin terms with the same meaning.

Reduction (complexity)

In computability theory and computational complexity theory, a reduction is an algorithm for transforming one problem into another problem. A reduction from one problem to another may be used to show that the second problem is at least as difficult as the first.

Intuitively, problem A is reducible to problem B if an algorithm for solving problem B efficiently (if it existed) could also be used as a subroutine to solve problem A efficiently. When this is true, solving A cannot be harder than solving B. "Harder" means having a higher estimate of the required computational resources in a given context (e.g., higher time complexity, etc.).

We write A ≤_m B, usually with a subscript on the ≤ to indicate the type of reduction being used (m : mapping reduction, p : polynomial reduction).

The mathematical structure generated on a set of problems by the reductions of a particular type generally forms a preorder, whose equivalence classes may be used to define degrees of unsolvability and complexity classes.