# Reduction

Reduction, reduced, or reduce may refer to:

## Science and technology

### Chemistry

• Reduction, part of a reduction-oxidation (redox) reaction in which atoms have their oxidation state changed.

### Computing and algorithms

• Reduction (complexity), a transformation of one problem into another problem
• 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?
• Bit Rate Reduction, an audio compression method
• Data reduction, simplifying data in order to facilitate analysis
• Graph reduction, an efficient version of non-strict evaluation
• L-reduction, a transformation of optimization problems which keeps the approximability features
• Partial order reduction, a technique for reducing the size of the state-space to be searched by a model checking algorithm
• Strength reduction, a compiler optimization where a function of some systematically changing variable is calculated more efficiently by using previous values of the function
• Variance reduction, a procedure used to increase the precision of the estimates that can be obtained for a given number of iterations
• 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 computing, a CPU design philosophy favoring an instruction set reduced in size and complexity of addressing, to simplify implementation, instruction level parallelism, and compiling

### Pure mathematics and statistics

• Reducible as the opposite of irreducible (mathematics)
• 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
• Subject reduction or preservation, a rewrite of an expression that does not change its type
• Reduction of order, a technique for solving second-order ordinary differential equations
• Reduction of the structure group, for a ${\displaystyle G}$-bundle ${\displaystyle B}$ and a map ${\displaystyle H\to G}$ an ${\displaystyle H}$-bundle ${\displaystyle B_{H}}$ such that the pushout ${\displaystyle B_{H}\times _{H}G}$ is isomorphic to ${\displaystyle B}$
• 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 homology, a minor modification made to homology theory in algebraic topology, designed to make a point have all its homology groups zero
• Reduced product, a construction that generalizes both direct product and ultraproduct
• 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 ring, a ring with no non-zero nilpotent elements
• Reduced row echelon form, a certain reduced row echelon form of a matrix which completely and uniquely determines its row space
• Reduced word, in a free group, a word with no adjacent generator-inverse pairs

### 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 condition a mixed state must satisfy in order for it to be separable
• Reduced mass, the "effective" inertial mass appearing in the two-body problem of Newtonian mechanics
• Reduced properties (pressure, temperature, or volume) of a fluid, defined based on the fluid's critical point

## Philosophy

• Reduction (philosophy), the process by which one object, property, concept, theory, etc., is shown to be entirely dispensable in favor of another
• Reductionism, a range of philosophical systems
• Reductio ad absurdum, a form of argument in which a proposition is disproven by following its implications to an absurd consequence
• Eidetic reduction, a technique in the study of essences in phenomenology whose goal is to identify the basic components of phenomena
• Intertheoretic reduction, in philosophy of science, one theory makes predictions that perfectly or almost perfectly match the predictions of a second theory