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complexity theory, the compression theorem is an important theorem about the complexity of computable functions. The theorem states that there exists
Compression_theorem
classes is infinite. The compression theorem is an important theorem about the complexity of computable functions. The theorem states that there exists
Structural_complexity_theory
Speeding up Turing machines by increasing tape symbol complexity
alphabet with a larger one. Specifically, it depends on the tape compression theorem: If a language L {\displaystyle L} is accepted by a Turing machine
Linear_speedup_theorem
Establishes the limits to possible data compression
Shannon's source coding theorem (or noiseless coding theorem) establishes the statistical limits to possible data compression for data whose source is
Shannon's source coding theorem
Shannon's_source_coding_theorem
Venezuelan computer scientist
yields concrete results like the compression theorem, the gap theorem, the honesty theorem and the Blum speedup theorem. Some of his other work includes
Manuel_Blum
Compact encoding of digital data
coding theorem; domain-specific theories include algorithmic information theory for lossless compression and rate–distortion theory for lossy compression. These
Data_compression
Sufficiency theorem for reconstructing signals from samples
The Nyquist–Shannon sampling theorem is a theorem in the field of signal processing which serves as a fundamental bridge between continuous-time signals
Nyquist–Shannon sampling theorem
Nyquist–Shannon_sampling_theorem
Chomsky–Schützenberger representation theorem (formal language theory) Codd's theorem (relational model) Compression theorem (computational complexity theory
List_of_theorems
Data compression approach allowing perfect reconstruction of the original data
Lossless compression is a class of data compression that allows the original data to be perfectly reconstructed from the compressed data with no loss of
Lossless_compression
probability for long sequences is accepted, the Slepian–Wolf theorem shows that much better compression rate can be achieved. As long as the total rate of X {\displaystyle
Slepian–Wolf_coding
Lossless data compression scheme
encoding) is any lossless data compression method that attempts to approach the lower bound declared by Shannon's source coding theorem, which states that any
Entropy_coding
Axioms in computational complexity theory
{\displaystyle C[F]=\bigcup _{n\in \mathbb {N} }C[f(n,\cdot )]} . Compression theorem: Let g ( x , n ) {\displaystyle g(x,n)} be a total computable function
Blum_axioms
Algebraic expansion of powers of a binomial
algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial. According to the theorem, the power ( x
Binomial_theorem
Lossless data compression algorithms
entropy rate of the source. Similar theorems apply to other versions of LZ algorithm. LZ77 algorithms achieve compression by replacing repeated occurrences
LZ77_and_LZ78
Infinitely many prime numbers exist
Euclid's theorem is a fundamental statement in number theory that asserts that there are infinitely many prime numbers. It was first proven by Euclid
Euclid's_theorem
Condition for a mathematical function to map some value to itself
In mathematics, a fixed-point theorem is a result saying that a function F will have at least one fixed point (a point x for which F(x) = x), under some
Fixed-point_theorem
Subfield of automated reasoning and mathematical logic
Since the proofs generated by automated theorem provers are typically very large, the problem of proof compression is crucial, and various techniques aiming
Automated_theorem_proving
Mathematical folklore
In mathematical folklore, the "no free lunch" (NFL) theorem (sometimes pluralized) of David Wolpert and William Macready, alludes to the saying "no such
No_free_lunch_theorem
Dynamic Markov compression Gauss–Markov theorem Gauss–Markov process Markov blanket Markov boundary Markov chain Markov chain central limit theorem Additive
List of things named after Andrey Markov
List_of_things_named_after_Andrey_Markov
entropy Kullback–Leibler divergence lossless compression negentropy noisy-channel coding theorem (Shannon's theorem) principle of maximum entropy quantum information
Index of information theory articles
Index_of_information_theory_articles
Theorem
{\displaystyle \Phi (a)} is a compression of π ( a ) {\displaystyle \pi (a)} . It is therefore a corollary of Stinespring's theorem that every unital completely
Stinespring_dilation_theorem
Idealized thermodynamic cycle
in 1824 and expanded upon by others in the 1830s and 1840s. By Carnot's theorem, it provides an upper limit on the efficiency of any classical thermodynamic
Carnot_cycle
data compression well suited for image compression (sometimes also video compression and audio compression) Transform coding: type of data compression for
List_of_algorithms
In proof theory, an area of mathematical logic, proof compression is the problem of algorithmically compressing formal proofs. The developed algorithms
Proof_compression
Problem in information theory and communication
theoretical results in the lossy compression case are presented by Aaron D. Wyner and Jacob Ziv in 1976. Although the theorems on DSC were proposed on 1970s
Distributed_source_coding
Technique to compress data
type of optimal prefix code that is commonly used for lossless data compression. The process of finding or using such a code is Huffman coding, an algorithm
Huffman_coding
In thermodynamics and thermal physics, the Gouy–Stodola theorem is an important theorem for the quantification of irreversibilities in an open system
Gouy–Stodola_theorem
Topics referred to by the same term
Shannon's source coding theorem, which establishes the theoretical limits to lossless data compression Shannon–Hartley theorem, which establishes the theoretical
Shannon's_law
Characterises an iterated function system whose attractor is close to a given set
In mathematics, the collage theorem characterises an iterated function system whose attractor is close, relative to the Hausdorff metric, to a given set
Collage_theorem
Average uncertainty in variable's states
compressed message has less redundancy. Shannon's source coding theorem states a lossless compression scheme cannot compress messages, on average, to have more
Entropy_(information_theory)
Thermodynamic process in which no mass or heat is exchanged with surroundings
example, the compression of a gas within a cylinder of an engine is assumed to occur so rapidly that on the time scale of the compression process, little
Adiabatic_process
Unsolved problem in graph theory
arXiv:1402.6079 [math.MG]. Rubinstein, J.; Weng, J. (1997-03-01). "Compression Theorems and Steiner Ratios on Spheres". Journal of Combinatorial Optimization
Gilbert–Pollak_conjecture
yields concrete results like the compression theorem, the gap theorem, the honesty theorem and the Blum speedup theorem. Some of his other work includes
Science and technology in Venezuela
Science_and_technology_in_Venezuela
Measure of algorithmic complexity
by c. To determine the probability, divide by 2n. By the above theorem (§ Compression), most strings are complex in the sense that they cannot be described
Kolmogorov_complexity
Algorithm used in data compression
a manner that can be reversed to recover the original string. Since compression techniques such as move-to-front transform and run-length encoding are
Burrows–Wheeler_transform
Theoretical engine
practical high-compression air engine, its fuel injected near the end of the compression stroke and ignited by the heat of compression, capable by 1969
Carnot_heat_engine
Form of entropy encoding used in data compression
The theoretical limit on this compression is given by the entropy of the source, which Shannon's source coding theorem establishes as the minimum average
Arithmetic_coding
and redundancy of a source, and its relevance through the source coding theorem; the mutual information, and the channel capacity of a noisy channel, including
History_of_information_theory
American physicist
states. This is now known as Schumacher compression. This was the quantum analog of Shannon's noiseless coding theorem, and it helped to start the field known
Benjamin_Schumacher
Assessment of the audio output from an electronic device
reproduce it. In some cases, processing such as equalization, dynamic range compression or stereo processing may be applied to a recording to create audio that
Sound_quality
Theorem in functional analysis
In linear algebra and functional analysis, the min-max theorem, or variational theorem, or Courant–Fischer–Weyl min-max principle, is a result that gives
Min-max_theorem
Theorem used in structural analysis
In civil engineering and structural analysis Clapeyron's theorem of three moments (by Émile Clapeyron) is a relationship among the bending moments at
Theorem_of_three_moments
Theory about lossy data compression
information theory which provides the theoretical foundations for lossy data compression; it addresses the problem of determining the minimal number of bits per
Rate–distortion_theory
Structures that are optimal based on the criteria defined by A.G.M. Michell
{\displaystyle l_{p}} , f q {\displaystyle f_{q}} is the compression value in any compression element of length l q {\displaystyle l_{q}} and C {\displaystyle
Michell_structures
Decomposition of periodic functions
differentiable. ATS theorem Carleson's theorem Dirichlet kernel Discrete Fourier transform Fast Fourier transform Fejér's theorem Fourier analysis Fourier
Fourier_series
Certain vector fields are the sum of an irrotational and a solenoidal vector field
In physics and mathematics, the Helmholtz decomposition theorem or the fundamental theorem of vector calculus states that certain differentiable vector
Helmholtz_decomposition
Computer technology
Silence compression is an audio processing technique used to effectively encode silent intervals, reducing the amount of storage or bandwidth needed to
Silence_compression
3-manifolds, Bieberbach Theorem, Flat manifolds, Crystallographic groups Seifert fiber space Heegaard splitting Waldhausen conjecture Compression body Handlebody
List of geometric topology topics
List_of_geometric_topology_topics
Decomposition of a compact oriented 3-manifold by dividing it into two handlebodies
by replacing handlebodies with compression bodies. The gluing map is between the positive boundaries of the compression bodies. A closed curve is called
Heegaard_splitting
Logical formulation of graph properties
property specified within a particular type of logic, and methods for data compression based on finding logical sentences that are modeled by a unique graph
Logic_of_graphs
Function in discrete mathematics
the star denotes complex conjugation. The Plancherel theorem is a special case of Parseval's theorem and states: ∑ n = 0 N − 1 | x n | 2 = 1 N ∑ k = 0 N
Discrete_Fourier_transform
Technique used in signal processing and data compression
a widely used transformation technique in signal processing and data compression. It is used in most digital media, including digital images (such as
Discrete_cosine_transform
Topics referred to by the same term
(disambiguation) Squeeze theorem, in calculus Short squeeze and long squeeze, in the stock market SQUOZE, a 1958 punch-card data compression scheme Main Squeeze
Squeeze
Thermodynamic cycle for spark ignition piston engines
parallel isochoric processes (constant volume). The isentropic process of compression or expansion implies that there will be no inefficiency (loss of mechanical
Otto_cycle
Principle relating to fluid dynamics
that Bernoulli's theorem is responsible... Unfortunately, the 'dynamic lift' involved...is not properly explained by Bernoulli's theorem. Denker, John S
Bernoulli's_principle
statistical physics, data compression, error correcting codes and related subjects. 1872 – Ludwig Boltzmann presents his H-theorem, and with it the formula
Timeline of information theory
Timeline_of_information_theory
Result of differential geometry proved by Gauss
or tearing, in other words without extra tension, compression, or shear. An application of the theorem is seen when a flat object is somewhat folded or
Theorema_Egregium
In operator theory, a Toeplitz operator is the compression of a multiplication operator on the circle to the Hardy space. Let S 1 {\displaystyle S^{1}}
Toeplitz_operator
Audible defect generated during the recording or editing of a sound
artifact, and in some cases is the result of data compression (not to be confused with dynamic range compression, which also may create sonic artifacts). Often
Sonic_artifact
Both deterministic and nondeterministic machines can solve more problems given more space
In computational complexity theory, the space hierarchy theorems are separation results that show that both deterministic and nondeterministic machines
Space_hierarchy_theorem
Device or program that encodes/decodes audio data in some bitstream format
which interface to one or more multimedia players. Most modern audio compression algorithms are based on modified discrete cosine transform (MDCT) coding
Audio_codec
Israeli computer scientist
theorems related to the "Shannon–McMillan–Breiman theorem" (1992). These results relate to core topics in information theory. He applied Compression Algorithms
Ilan_Sadeh
In mathematics and theoretical computer science, entropy compression is an information theoretic method for proving that a random process terminates,
Entropy_compression
Fuglede's theorem Compression (functional analysis) Friedrichs extension Stone's theorem on one-parameter unitary groups Stone–von Neumann theorem Functional
List of functional analysis topics
List_of_functional_analysis_topics
British mathematician
credited for discovering the collage theorem. Iterated Systems was initially devoted to fractal image compression (epitomised by the Barnsley fern), and
Michael_Barnsley
Data compression
Transform coding is a type of data compression for "natural" data like audio signals or photographic images. The transformation is typically lossless
Transform_coding
Performance measure of a device that uses thermal energy
pump is more than 1. These values are further restricted by the Carnot theorem. In general, energy conversion efficiency is the ratio between the useful
Thermal_efficiency
Thermodynamic cycle
mixture only during the latter 70% to 80% of the compression stroke. During the initial part of the compression stroke, the piston pushes part of the fuel-air
Miller_cycle
Mathematical models of heat pumps and refrigeration
cycles can be classified as vapor compression, vapor absorption, gas cycle, or Stirling cycle types. The vapor-compression cycle is used by many refrigeration
Heat pump and refrigeration cycle
Heat_pump_and_refrigeration_cycle
Scientific study of digital information
coding theory into compression and transmission is justified by the information transmission theorems, or source–channel separation theorems that justify the
Information_theory
Study of the properties of codes and their fitness
respective fitness for specific applications. Codes are used for data compression, cryptography, error detection and correction, data transmission and
Coding_theory
Turing reduction Savitch's theorem Space hierarchy theorem Speed Prior Speedup theorem Subquadratic time Time hierarchy theorem Exponential hierarchy Polynomial
List of computability and complexity topics
List_of_computability_and_complexity_topics
Thermodynamic cycle
cycle mode. Atkinson produced three different designs that had a short compression stroke and a longer expansion stroke. The first Atkinson-cycle engine
Atkinson_cycle
Graph divided into two independent sets
size of the maximum matching; this is Kőnig's theorem. An alternative and equivalent form of this theorem is that the size of the maximum independent set
Bipartite_graph
Matrix decomposition
computing the SVD can be too computationally expensive and the resulting compression is typically less storage efficient than a specialized algorithm such
Singular_value_decomposition
Type of set in information theory
schemes like Shannon's source coding theorem and channel coding theorem are developed, enabling near-optimal data compression and reliable transmission over
Typical_set
Square root of the mean square
is often used as the comparator signal for compression, which produces a "smoothing" effect in compression by responding more slowly to sharp transients
Root_mean_square
Set of eigenvalues of a matrix
Here, I {\displaystyle I} is the identity operator. By the closed graph theorem, λ {\displaystyle \lambda } is in the spectrum if and only if the bounded
Spectrum (functional analysis)
Spectrum_(functional_analysis)
Shape with six sides
Conway criterion will tile the plane. Pascal's theorem (also known as the "Hexagrammum Mysticum Theorem") states that if an arbitrary hexagon is inscribed
Hexagon
Subset of artificial intelligence
and compression. A system that predicts the posterior probabilities of a sequence given its entire history can be used for optimal data compression (by
Machine_learning
In mathematics, the Earle–Hamilton fixed point theorem is a result in geometric function theory giving sufficient conditions for a holomorphic mapping
Earle–Hamilton fixed-point theorem
Earle–Hamilton_fixed-point_theorem
Shape with four equal sides and angles
number of equal-area triangles, a result of Monsky's theorem. Cross's theorem or Vecten's theorem states that, for a triangle formed by the sides of three
Square
Technique in numerical linear algebra
reduced rank. The problem is used for mathematical modeling and data compression. The rank constraint is related to a constraint on the complexity of
Low-rank_approximation
Unsolved problem in matrix analysis
norm on the left-hand side is the spectral operator 2-norm. Crouzeix's theorem, proved in 2007, states that: ‖ f ( A ) ‖ ≤ 11.08 sup z ∈ W ( A ) | f (
Crouzeix's_conjecture
Lossless data compression technique
In the field of data compression, Shannon coding, named after its creator, Claude Shannon, is a lossless data compression technique for constructing a
Shannon_coding
Topic in mathematics
to the concept of typical set used in theories of data compression. Roughly speaking, the theorem states that although there are many series of results
Asymptotic equipartition property
Asymptotic_equipartition_property
Alleged data encoding technique
kilobyte of data, a level of compression which is mathematically impossible according to Shannon's source coding theorem.[citation needed] Sloot demonstrated
Sloot_Digital_Coding_System
Probability distribution
which is positive. This is justified by considering the central limit theorem in the log domain (sometimes called Gibrat's law). The log-normal distribution
Log-normal_distribution
Mathematical signal manipulation by computers
signal processing, digital image processing, data compression, video coding, audio coding, image compression, signal processing for telecommunications, control
Digital_signal_processing
through compressions in the sense that the equivalence relation generated by compression has one equivalence class. The inverse of a compression is sometimes
Incompressible_surface
kilobyte of data, a level of compression which is mathematically impossible according to Shannon's source coding theorem. Contrary to his claims, the
List_of_spurious_inventions
Thermodynamic process that is reversible and adiabatic
An example of such an exchange would be an isentropic expansion or compression that entails work done on or by the flow. For an isentropic flow, entropy
Isentropic_process
Algorithm trading more space for lower time
compressed bitmap indices, where it is faster to work with compression than without compression. Storing only the SVG source of a vector image and rendering
Space–time_tradeoff
Tool used in probabilistic polynomial identity testing
finite field version of this bound was proved by Øystein Ore in 1922. Theorem 1 (Schwartz, Zippel). Let P ∈ R [ x 1 , x 2 , … , x n ] {\displaystyle
Schwartz–Zippel_lemma
Aesthetic value of mathematics
; and Euclid's theorem that there are infinitely many prime numbers, which was also given by Hardy as an example of a beautiful theorem. Cantor's diagonal
Mathematical_beauty
If there are more items than boxes holding them, one box must contain at least two items
be used to prove that any lossless compression algorithm, provided it makes some inputs smaller (as "compression" suggests), will also make some other
Pigeonhole_principle
Engine combustion process
combustion engine. In it, fuel is ignited by heat generated during the compression of air in the combustion chamber, into which fuel is then injected. This
Diesel_cycle
Digital representation of sampled analog signals
developed to achieve further compression. Some of these techniques have been standardized and patented. Advanced compression techniques, such as modified
Pulse-code_modulation
Branch of civil engineering dealing with man-made structures
elastici", which contains his theorem for computing displacement as the partial derivative of the strain energy. This theorem includes the method of "least
Structural_engineering
Shape with three sides
An important tool for proving the existence of these points is Ceva's theorem, which gives a criterion for determining when three such lines are concurrent
Triangle
COMPRESSION THEOREM
COMPRESSION THEOREM
Girl/Female
Gujarati, Indian, Kannada, Tamil
Compassion
Girl/Female
Arabic
Compassion
Boy/Male
Hindu, Indian
Compassion
Girl/Female
Arabic, Muslim
Affection; Compassion
Boy/Male
Hindu, Indian, Marathi, Punjabi, Sikh, Telugu
Compassion
Boy/Male
Tamil
Compassion
Girl/Female
Indian
Compassion.
Boy/Male
Gujarati, Indian
Compassion
Boy/Male
Arabic
Effectiveness; Impression
Girl/Female
Hindu
Compassion, Mercy
Boy/Male
Arabic
Effectiveness; Impression
Girl/Female
Indian, Telugu
Compassion
Girl/Female
Tamil
Compassion, Mercy
Girl/Female
English Latin
Compassion; forbearance.
Girl/Female
Welsh
Impression.
Girl/Female
American, British, English, Latin
Compassion
Boy/Male
Arabic
Compassion; Kindness
Girl/Female
English Latin
Compassion; forbearance.
Girl/Female
Muslim
Compassion, Mercy
Girl/Female
African, Indian, Swahili
Compassion
COMPRESSION THEOREM
COMPRESSION THEOREM
Boy/Male
Indian
Light of the religion i.e. Islam
Boy/Male
Indian
Good
Male
Irish
Variant spelling of Irish Conchobar, CONCHOBOR means "hound-lover."
Boy/Male
Native American
Oldbark antelope.
Girl/Female
Arabic, Muslim
Name of a Sahabiyyah RA
Girl/Female
Indian
Noble sort
Boy/Male
Muslim
Loving
Boy/Male
Indian
Little full Moon
Boy/Male
Arabic American Muslim
Handsome.
Boy/Male
Indian, Punjabi, Sikh
One whose Heart is Holy
COMPRESSION THEOREM
COMPRESSION THEOREM
COMPRESSION THEOREM
COMPRESSION THEOREM
COMPRESSION THEOREM
n.
The pressure of the type on the paper, or the result of such pressure, as regards its appearance; as, a heavy impression; a clear, or a poor, impression; also, a single copy as the result of printing, or the whole edition printed at a given time.
n.
Compassion; pity; mercy.
n.
The act of pressing; compression; oppression.
n.
The act of oppressing, or state of being oppressed.
n.
The act of compressing, or state of being compressed.
n.
A sense of heaviness or obstruction in the body or mind; depression; dullness; lassitude; as, an oppression of spirits; an oppression of the lungs.
adv.
Without deep impression.
v. i.
To have compassion.
n.
A coming or bringing together, as in a public meeting, in a dispute, in the act of comparing, or in sexual intercourse.
n.
Dent; impression.
n.
A machine for compressing gases; especially, an air compressor.
p. pr & vb. n.
of Compress
n.
Compression.
n.
Remorse; compunction; compassion.
n.
An instrument for compressing an artery (esp., the femoral artery) or other part.
n.
Ravishment; rape.
n.
Oppression.
a.
Compressing, or having power or tendency to compress; as, a compressive force.
n.
That which oppresses; a hardship or injustice; cruelty; severity; tyranny.
n.
A print; impression.