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Reduction, reduced, or reduce may refer to:

Science and technology[edit]


Computing and algorithms[edit]

  • 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
  • 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[edit]

  • 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 -bundle and a map an -bundle such that the pushout is isomorphic to
  • 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
  • Variance reduction, a procedure used to increase the precision of the estimates that can be obtained for a given number of iterations


Medical procedures[edit]

Other uses in medicine[edit]


  • 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

Other uses in science and technology[edit]

Arts and media[edit]



  • 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


Other uses[edit]

See also[edit]