Definitions

# Reduction

[ri-duhk-shuhn]
Reduction, reduced, or reduce may refer to:

## Science

### Chemistry

• Reduction – chemical reaction in which atoms have their oxidation number (oxidation state) changed.

### Computing and algorithms

• Reduction (complexity) – a transformation of one problem into another problem.
• Graph reduction – an efficient version of non-strict evaluation
• Strength reduction – a compiler optimization where a function of some systematically changing variable is calculated more efficiently by using previous values of the function
• Reduction (recursion theory) – given sets A and B of natural numbers, is it possible to effectively convert a method for deciding membership in B into a method for deciding membership in A?
• L-reduction – a transformation of optimization problems which keeps the approximability features
• Variance reduction – a procedure used to increase the precision of the estimates that can be obtained for a given number of iterations
• Partial order reduction – a technique for reducing the size of the state-space to be searched by a model checking algorithm
• Bit Rate Reduction – an audio compression method
• Reduce (computer algebra system) – a general-purpose computer algebra system geared towards applications in physics
• Reduce (higher-order function) – in functional programming, a family of higher-order functions that process a data structure in some order and build up a return value
• Reduced instruction set computer – a CPU design philosophy that favors an instruction set reduced both in size and complexity of addressing modes, in order to enable easier implementation, greater instruction level parallelism, and more efficient compilers

### Pure mathematics and statistics

• Reduction (mathematics) – the rewriting of an expression into a simpler form
• Beta reduction – the rewriting of an expression from lambda calculus into a simpler form
• Dimension reduction – the process of reducing the number of random variables under consideration
• Lattice reduction – given an integer lattice basis as input, to find a basis with short, nearly orthogonal vectors
• Reduction of order – a technique for solving second-order ordinary differential equations
• Relation reduction – the extent to which a given relation is determined by an indexed family or a sequence of other relations, called the relation dataset
• Reduction of the structure group – for a $G$-bundle $B$ and a map $H to G$ an $H$-bundle $B_H$ such that the pushout $B_H times_H G$ is isomorphic to $B$
• Reduction system, reduction strategy, the application of rewriting systems to eliminate reducible expressions.
• Reduced form – in statistics, an equation which relates the endogenous variable X to all the available exogenous variables, both those included in the regression of interest (W) and the instruments (Z)
• Reduced ring – a ring with no non-zero nilpotent elements
• Reduced residue system – a set of φ(n) integers such that each integer is relatively prime to n and no two are congruent modulo n
• Reduced product – a construction that generalizes both direct product and ultraproduct
• Reduced word – in a free group, a word with no adjacent generator-inverse pairs
• Reduced homology – a minor modification made to homology theory in algebraic topology, designed to make a point have all its homology groups zero
• Reduced row echelon form – a certain reduced row echelon form of a matrix which completely and uniquely determines its row space

### Physics

• Dimensional reduction – the limit of a compactified theory where the size of the compact dimension goes to zero
• Reduction criterion – in quantum information theory, a necessary condtion a mixed state must satisfy in order for it to be separable
• Reduced temperature – of a fluid means the actual temperature, divided by its critical temperature
• Reduced mass – the "effective" inertial mass appearing in the two-body problem of Newtonian mechanics

## Philosophy

• Reduction (philosophy) – the process by which one object, property, concept, theory, etc., is shown to be entirely dispensable in favor of another
• Intertheoretic reduction – in philosophy of science, one theory makes predictions that perfectly or almost perfectly match the predictions of a second theory
• Eidetic reduction – a technique in the study of essences in phenomenology whose goal is to identify the basic components of phenomena

## History

• Lithic reduction – in Stone Age toolmaking, to detach lithic flakes from a lump of tool stone
• Reduction (Sweden) – return to the Crown of fiefs that had been granted to the Swedish nobility
• Indian Reductions – settlements in Spanish America intended to assimilate Indians

## Other

• Reduction (cooking) – the process of thickening or intensifying the flavor of a liquid mixture such as a soup, sauce, wine, or juice by evaporation
• Reduction to practice – in United States patent law, the embodiment of the concept of an invention
• Reduction in rank – military law
• Piano reduction – sheet music for the piano that was once music for other instruments that was reduced to its most basic components within a two line staff for piano
• Ego reduction – predicated on the use of Sigmund Freud's concept of the ego