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In proof theory, an area of mathematical logic, proof compression is the problem of algorithmically compressing formal proofs. The developed algorithms
Proof_compression
Subfield of automated reasoning and mathematical logic
always decidable. Since the proofs generated by automated theorem provers are typically very large, the problem of proof compression is crucial, and various
Automated_theorem_proving
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
In mathematical logic, proof compression by splitting is an algorithm that operates as a post-process on resolution proofs. It was proposed by Scott Cotton
Resolution proof compression by splitting
Resolution_proof_compression_by_splitting
In proof compression, an area of mathematical logic, LowerUnivalents is an algorithm used for the compression of propositional resolution proofs. LowerUnivalents
LowerUnivalents
Plumbing fitting
A compression fitting is a fitting used in plumbing and electrical conduit systems to join two tubes or thin-walled pipes together. In instances where
Compression_fitting
This proof compression method was presented as an algorithm named ReduceAndReconstruct, that operates as a post-processing of resolution proofs. ReduceAndReconstruct
Resolution proof reduction via local context rewriting
Resolution_proof_reduction_via_local_context_rewriting
In proof compression LowerUnits (LU) is an algorithm used to compress propositional logic resolution proofs. The main idea of LowerUnits is to exploit
LowerUnits
Lossless compression algorithm
programs and kernel panics). It was also used to create a proof-of-concept OpenZFS compression method which was integrated in 2020. The AWS Redshift and
Zstd
Cryptographic primitive
In cryptography, a one-way compression function is a function that transforms two fixed-length inputs into a fixed-length output. The transformation is
One-way_compression_function
Lossy and lossless image format
shortened to JXL) is an image format that supports both lossy and lossless compression. It was developed by the Joint Photographic Experts Group (JPEG), Google
JPEG_XL
Establishes the limits to possible data compression
coding theorem) establishes the statistical limits to possible data compression for data whose source is an independent identically-distributed random
Shannon's source coding theorem
Shannon's_source_coding_theorem
Data structure for storing non-overlapping sets
time per operation, each operation rebalances the structure (via tree compression) so that subsequent operations become faster. As a result, disjoint-set
Disjoint-set_data_structure
Mathematical concept
informal proof. He called this the "intrinsic de Bruijn Factor". The compression removes the effect that the length of identifiers in the proofs might have
De_Bruijn_factor
In mathematics and theoretical computer science, entropy compression is an information theoretic method for proving that a random process terminates,
Entropy_compression
American businessman
(Frost Proof). Application filed March 23, 1901; Patent issued to Philip Haas on February 10, 1903. US Patent # 720,022 - Frost Proof Compression. Application
Philip_Haas_(inventor)
Severely deficient supply of oxygen
brain damage. The asphyxia can be caused by facial compression, neck compression, or chest compression. This occurs mostly during restraint and handcuffing
Asphyxia
Alternative decimal expansion of 1
mathematically rigorous proofs. The intuitive arguments are generally based on properties of finite decimals that are extended without proof to infinite decimals
0.999...
Average uncertainty in variable's states
English; the PPM compression algorithm can achieve a compression ratio of 1.5 bits per character in English text. If a compression scheme is lossless
Entropy_(information_theory)
Cryptography secured against quantum computers
Post-quantum cryptography (PQC), sometimes referred to as quantum-proof, quantum-safe, or quantum-resistant, is the development of cryptographic algorithms
Post-quantum_cryptography
Category of mathematical proof
of problems cannot be solved. These are also known as proofs of impossibility, negative proofs, or negative results. Impossibility theorems often resolve
Proof_of_impossibility
Computer communications authentication algorithm
the compression function is a PRF. This recovers a proof based guarantee since no known attacks compromise the pseudorandomness of the compression function
HMAC
Set of cryptographic hash functions
They are built using the Merkle–Damgård construction, from a one-way compression function itself built using the Davies–Meyer structure from a specialized
SHA-2
In mathematical logic, proof compression by RecycleUnits is a method for compressing propositional logic resolution proofs. Its main idea is to make use
RecycleUnits
Sufficiency theorem for reconstructing signals from samples
optimal manner, as in a combined system of sampling and optimal lossy compression. This setting is relevant in cases where the joint effect of sampling
Nyquist–Shannon sampling theorem
Nyquist–Shannon_sampling_theorem
Overview of and topical guide to algorithms
cryptography, data compression, computer graphics, bioinformatics, and many other fields. The study of algorithms includes their design, proof of correctness
Outline_of_algorithms
Process to convert electric power into hydrogen or methane
combustion engine or can be injected into the local gas grid. The hydrogen compression and storage system stores up to 27 MWh of energy and increases the overall
Power-to-gas
Infinitely many prime numbers exist
Euclid in his work Elements. There are at least 200 proofs of the theorem. Euclid offered a proof in his work Elements (Book IX, Proposition 20), which
Euclid's_theorem
Measure of algorithmic complexity
ISBN 978-3-540-26877-2. Stated without proof in: P. B. Miltersen (2005). "Course notes for Data Compression - Kolmogorov complexity" (PDF). p. 7. Archived
Kolmogorov_complexity
data compression well suited for image compression (sometimes also video compression and audio compression) Transform coding: type of data compression for
List_of_algorithms
Appliance for cold food storage
a British patent in 1850 for a vapor compression system that used ether. The first practical vapor compression refrigeration system was built by James
Refrigerator
Both deterministic and nondeterministic machines can solve more problems given more space
{SPACE}}(f(n))={\mathsf {SPACE}}(O(f(n)))} because one can achieve any linear compression by switching to a larger alphabet. However, by measuring space in bits
Space_hierarchy_theorem
Reciprocating internal combustion engine
The 1.8L version is an inline 4-cylinder engine that carries a 10.5:1 compression ratio; the engine makes 133–138 PS (98–101 kW; 131–136 hp) at 6,000–6
Hyundai_Theta_engine
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
Aesthetic value of mathematics
indicate that various aspects of mathematics—including results, formulae, proofs and theories—can trigger subjective responses similar to the beauty of art
Mathematical_beauty
Magnetic tape data storage technology
data interchange and safe-keeping, like LTFS, WORM, encryption and data compression. Half-inch (12.65 mm) wide magnetic tape has been used for data storage
Linear_Tape-Open
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
Concept in coding theory
generalization to quantum code. Cover, Thomas M.; Thomas, Joy A. (2006), "Data Compression", Elements of Information Theory (2nd ed.), John Wiley & Sons, Inc, pp
Kraft–McMillan_inequality
Shape with three sides
tessellating arrangement triangles are not as strong as hexagons under compression (hence the prevalence of hexagonal forms in nature). Tessellated triangles
Triangle
Diving inside a protective cage to observe sharks in the wild
potentially dangerous shark species are present. In this application, the shark-proof cage may be used as a refuge, or as a diving stage during descent and ascent
Shark_cage_diving
Lydia's Scream against the cell wall glass of his cell, the subsequent compression causing the glass to crack, engineering his escape from his cell. In
List of Teen Wolf (2011 TV series) secondary characters
List_of_Teen_Wolf_(2011_TV_series)_secondary_characters
Diving mode and decompression technique
including decompression stress, high pressure nervous syndrome (HPNS), compression arthralgia, dysbaric osteonecrosis, oxygen toxicity, inert gas narcosis
Saturation_diving
Machine that washes dishes automatically
Brazing British Standard Pipe (BSP) Cast iron pipe Chemical drain cleaners Compression fitting Copper tubing Crimp (joining) Drain-waste-vent system Ductile
Dishwasher
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
Adaptation of the FIX protocol
In particular, it is a technology standard that offers significant compression capabilities for the transport of high-volume market data feeds and ultra
FAST_protocol
Algebraic expansion of powers of a binomial
ISBN 978-1-107-60174-1. Cover, Thomas M.; Thomas, Joy A. (1991). "Data Compression". Elements of Information Theory. Wiley. Ch. 5, pp. 78–124. doi:10.1002/0471200611
Binomial_theorem
Speeding up Turing machines by increasing tape symbol complexity
the 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
Hash function that is suitable for use in cryptography
blocks, and operating on them in sequence using a one-way compression function. The compression function can either be specially designed for hashing or
Cryptographic_hash_function
Joint pain caused by fast compression to high ambient pressure
Compression arthralgia is pain in the joints caused by exposure to high ambient pressure at a relatively high rate of compression, experienced by underwater
Compression_arthralgia
Size of a mathematical ball
constant x 2 + y 2 {\displaystyle x^{2}+y^{2}} ) that exactly matches the compression in the direction of the gradient of | z → | {\displaystyle |{\vec {z}}|}
Volume_of_an_n-ball
Video mode
July 2008, the ATSC standards were amended to include H.264/MPEG-4 AVC compression and 1080p at 50, 59.94 and 60 frames per second (1080p50 and 1080p60)
1080p
Result of differential geometry proved by Gauss
internal crumpling or tearing, in other words without extra tension, compression, or shear. An application of the theorem is seen when a flat object is
Theorema_Egregium
File format
three formats have support for compression, however only the PHAR format supports both per-file and whole archive compression. Zip and Tar formats only support
PHAR_(file_format)
Season of television series
Pied Piper, which is the result of Hendricks' development of a data compression algorithm. The season received positive reviews from critics. Thomas
Silicon_Valley_season_1
Species of beetle
to slide past each other, providing flexibility to absorb squishing compression. The second area is the puzzle-like design that runs the length of the
Phloeodes_diabolicus
Airtight seal
generally used for low-intensity applications such as in light bulb bases. "Compression seals" occur when the glass and the metal have different coefficients
Hermetic_seal
Technique for doubling the perceived frame rate of a video display
digital video transmission formats such as DV, DVB, and ATSC. New video compression standards like High Efficiency Video Coding are optimized for progressive
Interlaced_video
Italian model of sports car
engine with 350 PS (257 kW; 345 hp) DIN at 6000 rpm, thanks to a 11.0 : 1 compression ratio (versus 8.0 : 1 in the US market Pantera), larger Holley carburetors
De_Tomaso_Pantera
Extension to 3D film television standards
also known as MVC 3D) is a stereoscopic video coding standard for video compression that allows for encoding video sequences captured simultaneously from
Multiview_Video_Coding
American computer scientist
cryptography. He focuses on the topics of pseudorandomness and zero-knowledge proofs. His work on the zig-zag product, with Omer Reingold and Avi Wigderson,
Salil_Vadhan
Drug delivery form in which the ingredients are solidified for later consumption
that is easy to consume. Tablets are prepared either by moulding or by compression. The excipients can include diluents, binders or granulating agents,
Tablet_(pharmacy)
Metamorphic rock
the direction of metamorphic compression. The foliation in slate, called "slaty cleavage", is caused by strong compression in which fine-grained clay forms
Slate
Type of motorcycle
engine was a 99 cc (6.0 cu in) single cylinder air-cooled system. The compression ratio was 9.4:1 and the bore and stroke were 2.1 inches by 1.8 inches
Honda_XR100R
Cryptographic hash function
SHA-0 only by a single bitwise rotation in the message schedule of its compression function. According to the NSA, this was done to correct a flaw in the
SHA-1
Quantum-safe key encapsulation mechanism
Public key compression removed (due to NIST comments on the security proof) Parameter q reduced to 3329 (from 7681) Ciphertext compression parameters
ML-KEM
Entertaining object primarily used by children
thus suggested to promote children's development and healthy play. Age compression is a term used by some researchers and commentators to describe a perceived
Toy
Crewed full ocean depth rated submersible
gate carabiner Emergency locator beacon Rescue tether Safety helmet Shark-proof cage Snoopy loop Navigation equipment Distance line Diving compass Dive
DSV_Limiting_Factor
Modification of existing structures to make them more resistant to seismic activity
after the slab has set. This poststressing places the concrete under compression – a condition under which it is extremely strong in bending and so will
Seismic_retrofit
Sequence of numbers consisting of 1 and -1
_{i=1}^{k}x_{i\cdot d}\right|>C.} The Erdős discrepancy problem asks for a proof or disproof of this conjecture. In February 2014, Alexei Lisitsa and Boris
Sign_sequence
Read-only optical disc for high-fidelity audio storage
requirements of DSD, a lossless data compression method called Direct Stream Transfer (DST) is used. DST compression is compulsory for multi-channel regions
Super_Audio_CD
Post-quantum digital signature scheme
also decrease the key and signature sizes using tree-less WOTS+ key compression, the addition of the R parameter during signing and the replacement of
SPHINCS+
Cryptographic protocols for securing data in transit
successfully defended against by turning off TLS compression or SPDY header compression, BREACH exploits HTTP compression which cannot realistically be turned off
Transport_Layer_Security
Tool used in probabilistic polynomial identity testing
S | n − 1 . {\displaystyle |Z(P)\cap S^{n}|\leq d\cdot |S|^{n-1}.} Proof. The proof is by mathematical induction on n. For n = 1, P can have at most d
Schwartz–Zippel_lemma
Method of building collision-resistant cryptographic hash functions
collision-resistant cryptographic hash functions from collision-resistant one-way compression functions. This construction was used in the design of many popular hash
Merkle–Damgård_construction
redundant proof is a proof that has a subset that is a shorter proof of the same result. In other words, a proof is redundant if it has more proof steps than
Redundant_proof
Sagging of the female breast
bras, in which each cup is separately molded, are more effective than compression-type bras, which press the breasts close to the body, at reducing total
Ptosis_(breasts)
infrastructure in combat and the condition of his weaponry. Blowpipe Compression cannon The Rebirth (Part 2,3) John Moschitta, Jr. The conniving brother-in-law
List of The Transformers characters
List_of_The_Transformers_characters
2023 death in New York City, U.S.
the medical examiner's office ruled that Neely's death was homicide by compression of the neck. A week after that, Penny was charged with second-degree
Killing_of_Jordan_Neely
Subfield of artificial intelligence
reasoning capabilities, neuro-symbolic AI promises to achieve network compression via knowledge reuse. This is the opposite of the usual scaling-up of
Neuro-symbolic_AI
Topics referred to by the same term
an online list of points of a triangle Ericsson Texture Compression, an image compression algorithm /etc, a directory in Unix-like systems, see Unix
ETC
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
Voronoi tessellation where the generating point of each Voronoi cell is also its centroid
Euclidean space. Centroidal Voronoi tessellations are useful in data compression, optimal quadrature, optimal quantization, clustering, and optimal mesh
Centroidal Voronoi tessellation
Centroidal_Voronoi_tessellation
Graph partition into regular subgraphs
theoretical, some attempts have been made to use the regularity method as compression technique for large graphs. A different notion of regularity was introduced
Szemerédi_regularity_lemma
1954 U.S. thermonuclear weapon test in the Marshall Islands
equally applying pressure with the tamper. The compression factor of the fusion fuel and its adiabatic compression energy determined the minimal energy required
Castle_Bravo
Uniform address for services on a website
HTTP Persistence Compression HTTPS QUIC Request methods OPTIONS GET HEAD POST PUT DELETE TRACE CONNECT PATCH Header fields Cookie ETag Location HTTP referer
Well-known_URI
Messaging and VoIP service owned by Meta
discrete cosine transform (MDCT) and linear predictive coding (LPC) audio compression algorithms. WhatsApp uses Opus at 8–16 kHz sampling rates. On November
Family of cryptographic hash functions
does not reduce security, it makes a formal security proof impossible. We start with a compression function ϕ {\displaystyle \phi } with parameters n
Fast_syndrome-based_hash
Plane curve: conic section
bending. Similarly, the structures of parabolic arches are purely in compression. Paraboloids arise in several physical situations as well. The best-known
Parabola
Israeli software company
Ethereum using a file of 80 kilobytes, which acts as a proof for the content in the batch. This compression process increases the amount of data that can be
StarkWare_Industries
System of rules to convert information into another form or representation
these codes was to save on cable costs. The use of data coding for data compression predates the computer era; an early example is the telegraph Morse code
Code
American novelist and underwater explorer (1931–2020)
Barodontalgia Dental barotrauma Middle ear barotrauma Pulmonary barotrauma Compression arthralgia Decompression illness Dysbarism Oxygen Freediving blackout
Clive_Cussler
Numbers obtained by adding the two previous ones
Fibonacci numbers. The Fibonacci number series is used for optional lossy compression in the IFF 8SVX audio file format used on Amiga computers. The number
Fibonacci_sequence
Concrete with rebar
not. Reinforced concrete may also be permanently stressed (concrete in compression, reinforcement in tension), so as to improve the behavior of the final
Reinforced_concrete
1993 video game
the video display processor, creating better results than the Cinepak compression used for other Sega CD games. The special stages feature Mode 7-like
Sonic_CD
Reciprocating internal combustion engine
stroke creating a displacement of 444 cu in (7.3 L). It has a 17.5:1 compression ratio, and a dry weight of approximately 920 lb (417 kg). This engine
Ford_Power_Stroke_engine
AI that generates content
using consumer-grade gaming graphics cards through such techniques as compression. Language models with hundreds of billions of parameters, such as GPT-4
Generative_AI
Condition for a mathematical function to map some value to itself
theorems in infinite-dimensional spaces. The collage theorem in fractal compression proves that, for many images, there exists a relatively small description
Fixed-point_theorem
Engine with large amounts of ceramics
engines allow for the compression and expansion of gases at extremely high temperatures without loss of heat or engine damage. Proof-of-concept ceramic engines
Ceramic_engine
Mechanical device that changes the direction or magnitude of a force
hitting it with a sledge hammer, forcing the sides apart, but no amount of compression force from the wood walls will cause it to pop back out of the block
Simple_machine
Formation of a quasi-liquid film on the surface of a solid
that expansion of water as it freezes implied that ice should melt upon compression. This idea was exploited by John Joly as a mechanism for ice skating
Premelting
PROOF COMPRESSION
PROOF COMPRESSION
Boy/Male
Arabic
Proof; Evidence
Girl/Female
Arabic, Muslim
Guide; Proof
Boy/Male
Muslim
Proof
Boy/Male
Muslim/Islamic
Proof
Boy/Male
Indian
Proof
Boy/Male
Indian
Argument, Reasoning, Proof
Boy/Male
Indian
Proof
Boy/Male
Arabic, Muslim
The Proof
Boy/Male
Muslim
Evidence. Proof.
Boy/Male
Arabic, Muslim
Evidence; Proof
Girl/Female
Muslim/Islamic
Guide Proof
Boy/Male
Muslim
Proof
Girl/Female
Indian
Witness; Proof
Boy/Male
Muslim/Islamic
Proof
Boy/Male
Afghan, Arabic, Hindu, Indian, Muslim
Proof
Surname or Lastname
English
English : variant of Rolfe.German : from Ruffo, a short form of a personal name formed with hrÅd ‘renown’, ‘victory’.Probably an Americanized spelling of German Ruf and Ruff.
Boy/Male
Arabic, French, German, Gujarati, Hindu, Indian, Malaysian, Muslim, Turkish
Proof; Evidence
Girl/Female
Muslim
Proof
Girl/Female
Muslim
Guide, Proof
Boy/Male
Muslim
Argument, Reasoning, Proof
PROOF COMPRESSION
PROOF COMPRESSION
Biblical
Tabeel, good God
Girl/Female
Tamil
Daritree | தரீதà¯à®°à¯€
Earth
Boy/Male
Hindu, Indian
Who is Never Lose; Live Forever
Girl/Female
Hindu
Same as Gayatri
Boy/Male
Celebrity, Gujarati, Hindu, Indian, Jain, Kannada, Malayalam, Marathi, Telugu
Couple; Also a Name of Lord Krishna from his Millions Name
Boy/Male
Hindu
Reviver of dead monkeys
Girl/Female
American, Australian, British, Chinese, Christian, Danish, Dutch, English, French, German, Indian, Irish, Latin, Netherlands
Song of Joy; Song of Happiness; Womanly; Form of Carolyne
Boy/Male
Arabic, Muslim
Slave of the Propitious / Benefactor
Boy/Male
Tamil
Lord venkateswara
Girl/Female
American, Australian, British, English, French
God is Gracious; God has Answered; Name of a Plant
PROOF COMPRESSION
PROOF COMPRESSION
PROOF COMPRESSION
PROOF COMPRESSION
PROOF COMPRESSION
v. t.
Armor of excellent or tried quality, and deemed impenetrable; properly, armor of proof.
n.
Proof.
n.
That which resembles, or corresponds to, the covering or the ceiling of a house; as, the roof of a cavern; the roof of the mouth.
n.
A trial impression, as from type, taken for correction or examination; -- called also proof sheet.
a.
Proof against proofs; obstinate in the wrong.
a.
Firm or successful in resisting; as, proof against harm; waterproof; bombproof.
v. t.
To arm with proof armor; to arm securely; as, to proof-arm herself.
n.
Proof.
n.
Trial; proof.
n.
Proof.
n.
Proof.
n.
Demonstration; proof.
n.
Proof; trial.
n.
Proof; evidence.
n.
The cover of any building, including the roofing (see Roofing) and all the materials and construction necessary to carry and maintain the same upon the walls or other uprights. In the case of a building with vaulted ceilings protected by an outer roof, some writers call the vault the roof, and the outer protection the roof mask. It is better, however, to consider the vault as the ceiling only, in cases where it has farther covering.
a.
Highly rectified; very strongly alcoholic; as, high-proof spirits.
a.
Used in proving or testing; as, a proof load, or proof charge.
v. t.
To cover with a roof.