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What (who) is reduction system - definition

REPLACING SUBTERM IN A FORMULA WITH ANOTHER TERM

Term rewriting; Term rewriting system; Term-rewriting; Rewrite system; Rewrite rule; Phase-structure rule; Rewriting system; Term Rewriting System; Reducible expression; Redex; Rewrite rules; Transformational rule; Rewriting logic; Term rewrite system; Reduction system; Substitution system; Reduction systems; Termination (term rewriting); Termination (rewriting); Trace rewriting system; Tree rewriting; Rewriter

$'''Pic.2:''' Rule lhs term <math>x*(y*z)</math> matching in term <math>\frac{a*((a+1)*(a+2))}{1*(2*3)}</math>$
$'''Pic.1:''' Schematic triangle diagram of application of a rewrite rule <math>l \longrightarrow r</math> at position <math>p</math> in a term, with matching substitution <math>\sigma</math>$

Drag reduction system

FORM OF DRIVER ADJUSTABLE BODYWORK AIMED AT REDUCING AERODYNAMIC DRAG IN ORDER TO INCREASE STRAIGHT LINE TOP SPEED AND PROMOTE OVERTAKING, WHILE PROVIDING GRIP IN CORNERS

Drag Reduction System; DRS Zone; Drag Reduction Systems

In motor racing, the drag reduction system (DRS) is a form of driver-adjustable bodywork aimed at reducing aerodynamic drag in order to increase top speed and promote overtaking. It is an adjustable rear wing of the car, which moves in response to driver commands.

https://en.wikipedia.org/wiki/Drag_reduction_system

Dolby noise-reduction system

A LINE OF NOISE REDUCTION SYSTEMS FOR REEL-TO-REEL AND CASSETTE TAPE RECORDERS

Dolby Noise Reduction; Dolby-B Noise Reduction; Dolby-B; Dolby NR; Dolby noise reduction; Dolby A; Type A Dolby Noise Reduction; Dolby B; Dolby C; Dolby S; Dolby HX Pro; HX Pro; Dolby noise reduction system; Dolby FM; Dolby HX; Play Trim; Dolby Play Trim; NAD Play Trim; RFZ V723; V723; RMS (noise reduction); Rauschminderungssystem; RFT RMS; RFT Rauschminderungssystem; RMS (RFT); Dolby (noise reduction)

A Dolby noise-reduction system, or Dolby NR, is one of a series of noise reduction systems developed by Dolby Laboratories for use in analog audio tape recording. The first was Dolby A, a professional broadband noise reduction system for recording studios in 1965, but the best-known is Dolby B (introduced in 1968), a sliding band system for the consumer market, which helped make high fidelity practical on cassette tapes, which used a relatively noisy tape size and speed.

https://en.wikipedia.org/wiki/Dolby_noise-reduction_system

Dimensionality reduction

PROCESS OF REDUCING THE NUMBER OF RANDOM VARIABLES UNDER CONSIDERATION

Dimension reduction; Dimensionality Reduction; Dimensionality reduction algorithm; Linear dimensionality reduction

Dimensionality reduction, or dimension reduction, is the transformation of data from a high-dimensional space into a low-dimensional space so that the low-dimensional representation retains some meaningful properties of the original data, ideally close to its intrinsic dimension. Working in high-dimensional spaces can be undesirable for many reasons; raw data are often sparse as a consequence of the curse of dimensionality, and analyzing the data is usually computationally intractable (hard to control or deal with).

https://en.wikipedia.org/wiki/Dimensionality_reduction

Wikipedia

Rewriting

In mathematics, computer science, and logic, rewriting covers a wide range of methods of replacing subterms of a formula with other terms. Such methods may be achieved by rewriting systems (also known as rewrite systems, rewrite engines, or reduction systems). In their most basic form, they consist of a set of objects, plus relations on how to transform those objects.

Rewriting can be non-deterministic. One rule to rewrite a term could be applied in many different ways to that term, or more than one rule could be applicable. Rewriting systems then do not provide an algorithm for changing one term to another, but a set of possible rule applications. When combined with an appropriate algorithm, however, rewrite systems can be viewed as computer programs, and several theorem provers and declarative programming languages are based on term rewriting.

https://en.wikipedia.org/wiki/Rewriting

Examples of use of reduction system

1. Outdoor photographers will appreciate the 1Ds Mark III‘s dust reduction system.

2. The parking lot will have two entrances and exits; 60 more parking spaces will be built inside the museum compound for the hall‘s use and the building will be acoustically designed and insulated against noise, with a sound reduction system.