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HARDNESS

  • Mohs scale
  • Classification framework for scratch resistance

    The Mohs scale (/moʊz/ MOHZ[citation needed]) of mineral hardness is a qualitative ordinal scale, from 1 to 10, characterizing scratch resistance of minerals

    Mohs scale

    Mohs scale

    Mohs_scale

  • Hardness
  • Measure of a material's resistance to localized plastic deformation

    In materials science, hardness (antonym: softness) is a measure of the resistance to localized plastic deformation, such as an indentation (over an area)

    Hardness

    Hardness

  • Hard water
  • Water that has a high mineral content

    content. It can pose critical problems in industrial settings, where water hardness is monitored to avoid problematic limescaling in boilers, cooling towers

    Hard water

    Hard water

    Hard_water

  • Brinell hardness test
  • Brinell scale of hardness

    The Brinell hardness test (pronounced /brəˈnɛl/) measures the indentation hardness of materials. It determines hardness through the scale of penetration

    Brinell hardness test

    Brinell hardness test

    Brinell_hardness_test

  • Vickers hardness test
  • Hardness test

    The Vickers hardness test was developed in 1921 by Robert L. Smith and George E. Sandland at Vickers Ltd as an alternative to the Brinell method to measure

    Vickers hardness test

    Vickers hardness test

    Vickers_hardness_test

  • Rockwell hardness test
  • Hardness scale

    The Rockwell hardness test is a hardness test based on indentation hardness of a material. The Rockwell test measures the depth of penetration of an indenter

    Rockwell hardness test

    Rockwell hardness test

    Rockwell_hardness_test

  • Janka hardness test
  • Test to measure resistance of wood

    The Janka hardness test (English: /ˈdʒæŋkə/; German: [ˈjaŋka]), created by Austrian-born American researcher Gabriel Janka (1864–1932), measures the resistance

    Janka hardness test

    Janka hardness test

    Janka_hardness_test

  • Hardness scales
  • Topics referred to by the same term

    Hardness scales may refer to: Scratch hardness The Mohs scale of mineral hardness The Vickers hardness test The Brinell scale The Janka hardness test The

    Hardness scales

    Hardness_scales

  • Erection Hardness Score
  • Patient-reported outcome for scoring erection hardness

    The Erection Hardness Score (EHS) is a single-item Likert scale used to assess the subjective hardness of the penis as reported by the patient. It ranges

    Erection Hardness Score

    Erection_Hardness_Score

  • Hardness of approximation
  • hardness of approximation is a field that studies the algorithmic complexity of finding near-optimal solutions to optimization problems. Hardness of

    Hardness of approximation

    Hardness_of_approximation

  • Pencil
  • Writing implement

    were then fired in a kiln. By varying the ratio of graphite to clay, the hardness of the graphite rod could also be varied. This method of manufacture, which

    Pencil

    Pencil

    Pencil

  • Computational hardness assumption
  • Hypothesis in computational complexity theory

    In computational complexity theory, a computational hardness assumption is the hypothesis that a particular problem cannot be solved efficiently (where

    Computational hardness assumption

    Computational_hardness_assumption

  • Hot hardness
  • engineering and metallurgy, hot hardness or red hardness (when a metal glows a dull red from the heat) corresponds to hardness of a material at high temperatures

    Hot hardness

    Hot_hardness

  • Scratch hardness
  • Any measure of hardness based on scratch resistance

    Scratch hardness refers to the hardness of a material in terms of resistance to scratches and abrasion by a harder material forcefully drawn over its

    Scratch hardness

    Scratch_hardness

  • Indentation hardness
  • Any measure of hardness based on indentation resistance

    Indentation hardness tests are used in mechanical engineering to determine the hardness of a material to deformation. Several such tests exist, wherein

    Indentation hardness

    Indentation_hardness

  • Shore durometer
  • Hardness-testing device

    The Shore durometer is a device for measuring the hardness of a material, typically of polymers. Higher numbers on the scale indicate a greater resistance

    Shore durometer

    Shore durometer

    Shore_durometer

  • Knoop hardness test
  • Test for mechanical hardness

    The Knoop hardness test /kəˈnuːp/ is a microhardness test – a test for mechanical hardness used particularly for very brittle materials or thin sheets

    Knoop hardness test

    Knoop hardness test

    Knoop_hardness_test

  • Carbonate hardness
  • Measure of water hardness

    Carbonate hardness, is a measure of the water hardness caused by the presence of carbonate (CO2− 3) and bicarbonate (HCO− 3) anions. Carbonate hardness is usually

    Carbonate hardness

    Carbonate_hardness

  • Diamond
  • Form of carbon

    it at a negligible rate under those conditions. Diamond has the highest hardness and thermal conductivity of any natural material, properties that are used

    Diamond

    Diamond

    Diamond

  • Roll hardness tester
  • A roll hardness tester is a device to measure the roll hardness, hardness profile and hardness variation of paper rolls. In the preparation phase, the

    Roll hardness tester

    Roll_hardness_tester

  • Corundum
  • Oxide mineral

    (ruby-sapphire) (appearing in Sanskrit as kuruvinda). Because of corundum's hardness (pure corundum is defined to have 9.0 on the Mohs scale), it can scratch

    Corundum

    Corundum

    Corundum

  • Barcol hardness test
  • The Barcol hardness test characterizes the indentation hardness of materials through the depth of penetration of an indentor, loaded on a material sample

    Barcol hardness test

    Barcol_hardness_test

  • Tablet hardness testing
  • Tablet hardness testing is a laboratory technique used by the pharmaceutical industry to determine the breaking point and structural integrity of a tablet

    Tablet hardness testing

    Tablet_hardness_testing

  • DGH
  • Unit of water hardness

    Degrees of general hardness (dGH or °GH) is a unit of water hardness, specifically of general hardness. General hardness is a measure of the concentration

    DGH

    DGH

  • Hard
  • Topics referred to by the same term

    dictionary. Hard means something that is difficult to do. It may also refer to: Hardness, resistance of physical materials to deformation or fracture Hard water

    Hard

    Hard

  • Leopard 1
  • Main battle tank family of German origin

    The Kampfpanzer Leopard, subsequently Leopard 1 following the introduction of the successive Leopard 2, is a main battle tank designed by Porsche, and

    Leopard 1

    Leopard 1

    Leopard_1

  • Abrasion resistant steel
  • High carbon steel

    cooled, which is the tempering phase. The hardness of abrasion resistant steel is determined by a Brinell hardness test. This test uses a small steel ball

    Abrasion resistant steel

    Abrasion_resistant_steel

  • NP-hardness
  • Complexity class

    In computational complexity theory, a computational problem H is called NP-hard if, for every problem L which can be solved in non-deterministic polynomial-time

    NP-hardness

    NP-hardness

    NP-hardness

  • Tempering (metallurgy)
  • Process of heat treating used to increase the toughness of iron-based alloys

    iron, to achieve greater toughness by decreasing the hardness of the alloy. The reduction in hardness is usually accompanied by an increase in ductility

    Tempering (metallurgy)

    Tempering (metallurgy)

    Tempering_(metallurgy)

  • Calcite
  • Calcium carbonate mineral

    component of limestone. Calcite defines hardness 3 on the Mohs scale of mineral hardness, based on scratch hardness comparison. Large calcite crystals are

    Calcite

    Calcite

    Calcite

  • Gypsum
  • Soft calcium sulfate mineral

    [citation needed] The Mohs scale of mineral hardness defines gypsum as hardness value 2 based on scratch hardness comparison. Fine-grained white or lightly

    Gypsum

    Gypsum

    Gypsum

  • Meyer hardness test
  • The Meyer hardness test is a hardness test based upon projected area of an impression. The hardness, H {\displaystyle H} , is defined as the maximum load

    Meyer hardness test

    Meyer hardness test

    Meyer_hardness_test

  • The Hardness of the World
  • 1977 studio album by Slave

    The Hardness of the World is the second album by the American funk band Slave, released in 1977, their second album release that year. The lead single

    The Hardness of the World

    The_Hardness_of_the_World

  • Superhard material
  • Material with Vickers hardness exceeding 40 gigapascals

    superhard material is a material with a hardness value exceeding 40 gigapascals (GPa) when measured by the Vickers hardness test. They are virtually incompressible

    Superhard material

    Superhard material

    Superhard_material

  • Mineral
  • Crystalline chemical element or compound formed by geologic processes

    species usually includes its common physical properties such as habit, hardness, lustre, diaphaneity, colour, streak, tenacity, cleavage, fracture, system

    Mineral

    Mineral

    Mineral

  • DKH
  • Degrees of German carbonate hardness (°dKH or °KH; the dKH is from the German deutsche Karbonathärte) is a unit of water hardness, specifically for temporary

    DKH

    DKH

  • Hardness comparison
  • Standard hardness conversion table

    Vickers Hardness, Rockwell Hardness, Superficial Hardness, Knoop Hardness, Scleroscope Hardness, and Leeb Hardness" (2019) Hardness Conversion Table – Brinell

    Hardness comparison

    Hardness_comparison

  • Hardnesses of the elements (data page)
  • Hardness can vary by several hundred percent depending on the pretreatment, see e.g. Iron#Mechanical properties and Angelo Basile; Fausto Gallucci (2011)

    Hardnesses of the elements (data page)

    Hardnesses_of_the_elements_(data_page)

  • Marble
  • Type of metamorphic rock

    impurities are redistributed and recrystallized during metamorphism. Due to its hardness, durability and resistance to temperature, marble is often used in sculpture

    Marble

    Marble

    Marble

  • Moissanite
  • Silicon carbide mineral

    moissanite is useful for commercial and industrial applications due to its hardness, optical properties, and thermal conductivity. The mineral moissanite was

    Moissanite

    Moissanite

    Moissanite

  • Neue Deutsche Härte
  • Subgenre of rock music

    Neue Deutsche Härte (German: [ˈnɔʏə ˈdɔʏtʃə ˈhɛʁtə]; lit. "New German Hardness", sometimes abbreviated as NDH), also known as dance-metal, is a crossover

    Neue Deutsche Härte

    Neue Deutsche Härte

    Neue_Deutsche_Härte

  • Rhenium diboride
  • Chemical compound

    Rhenium diboride (ReB2) is a synthetic high-hardness material that was first made in 1962. The compound is formed from a mixture of rhenium, noted for

    Rhenium diboride

    Rhenium diboride

    Rhenium_diboride

  • HSAB theory
  • Chemical theory about acids and bases

    relative ordering of ligands and transition metal ions in terms of their hardness and softness. HSAB theory is also useful in predicting the products of

    HSAB theory

    HSAB_theory

  • High-speed steel
  • Subset of tool steels

    steels can withstand higher temperatures without losing their temper (hardness), allowing use of faster cutting speeds. At room temperature, in their

    High-speed steel

    High-speed steel

    High-speed_steel

  • Lattice-based cryptography
  • Cryptographic primitives that involve lattices

    lattice-based cryptographic construction whose security could be based on the hardness of well-studied lattice problems, and Cynthia Dwork showed that a certain

    Lattice-based cryptography

    Lattice-based_cryptography

  • Dartmouth, Devon
  • Town in Devon, England

    was used as an unofficial footpath linking Clifton, to the south, with Hardness, to the north. Before this it was necessary to go westwards to the head

    Dartmouth, Devon

    Dartmouth, Devon

    Dartmouth,_Devon

  • Cast iron
  • Iron-carbon alloy

    bulk hardness of the cast iron simply by virtue of their own very high hardness and their substantial volume fraction, such that the bulk hardness can

    Cast iron

    Cast iron

    Cast_iron

  • Aluminium oxide
  • Chemical compound

    used as feedstock to produce aluminium metal, as an abrasive owing to its hardness, and as a refractory material owing to its high melting point. Corundum

    Aluminium oxide

    Aluminium oxide

    Aluminium_oxide

  • Quartz
  • Mineral made of silicon and oxygen

    defining the value of 7 on the Mohs scale of hardness, a qualitative scratch method for determining the hardness of a material. The word quartz is derived

    Quartz

    Quartz

    Quartz

  • Gregory Peck
  • American actor (1916–2003)

    Gregory Peck.... Peck does an extraordinarily able job in revealing the hardness and the softness of a general exposed to peril." Film historian Peter von

    Gregory Peck

    Gregory Peck

    Gregory_Peck

  • Talc
  • Phyllosilicate mineral in the pyrophyllite-talc group

    platy form. The Mohs scale of mineral hardness, based on scratch hardness comparison, defines value 1 as the hardness of talc, the softest mineral. When

    Talc

    Talc

    Talc

  • Water
  • Chemical compound of hydrogen and oxygen

    safety of food, but also the preservation and shelf life of food. Water hardness is also a critical factor in food processing and may be altered or treated

    Water

    Water

    Water

  • Radiation hardening
  • Making devices resist ionizing radiation

    radiation-hardened versions (RadHard). While SOI eliminates latchup events, TID and SEE hardness are not guaranteed to be improved. Choosing a substrate with wide band

    Radiation hardening

    Radiation_hardening

  • Lonsdaleite
  • Hexagonal lattice allotrope of carbon

    natural specimens exhibited somewhat lower hardness through a large range of values (from 7–8 on Mohs hardness scale). The cause is speculated to be due

    Lonsdaleite

    Lonsdaleite

    Lonsdaleite

  • Fluorite
  • Mineral form of calcium fluoride

    isometric forms are not uncommon. The Mohs scale of mineral hardness, based on scratch hardness comparison, defines value 4 as fluorite. Pure fluorite is

    Fluorite

    Fluorite

    Fluorite

  • Carbon steel
  • Steel in which the main interstitial alloying constituent is carbon

    suitable for welding, but can be heat treated to improve its strength, hardness, and durability. Carbon steel is susceptible to rust and corrosion, especially

    Carbon steel

    Carbon steel

    Carbon_steel

  • Amethyst
  • Mineral, quartz variety

    structure is quite rigid and results in quartz's hardness and resistance to weathering. The hardness of the mineral is the same as quartz, thus making

    Amethyst

    Amethyst

    Amethyst

  • Tungsten
  • Chemical element with atomic number 74 (W)

    tungsten arc welding, superalloys, and radiation shielding. Tungsten's hardness and high density make it suitable for military applications in penetrating

    Tungsten

    Tungsten

    Tungsten

  • Olivia Newton-John
  • British–Australian singer (1948–2022)

    Angeles Times offers a counterpoint on her career decline in the mid-1980s: "Hardness never was Newton-John's comfort zone, though, and the 1980s were a much

    Olivia Newton-John

    Olivia Newton-John

    Olivia_Newton-John

  • Citrine
  • Transparent, yellow variety of quartz

    visually, but they differ in hardness. All quartz varieties have a hardness of 7 on the Mohs scale, while topaz has a hardness of 8. Citrine can also be

    Citrine

    Citrine

    Citrine

  • Blue diamond
  • Blue-colored variant of a diamond

    blue color in the stone. The Mohs hardness of a blue diamond is around the same as a regular diamond, with a hardness of 10. They are colored blue by trace

    Blue diamond

    Blue diamond

    Blue_diamond

  • Cutting tool material
  • Materials used in cutting tools

    Their hardness is sufficient to machine other steels. Carbon tool steels: They lose their hardness at 200 °C High speed steels: They lose their hardness at

    Cutting tool material

    Cutting_tool_material

  • Periodic table
  • Tabular arrangement of the chemical elements

    "Should negative electron affinities be used for evaluating the chemical hardness?". Physical Chemistry Chemical Physics. 13 (6): 2285–2293. doi:10.1039/C0CP01785J

    Periodic table

    Periodic table

    Periodic_table

  • Cutting
  • Partial or complete separation of a body or system into two or more parts

    However, any sufficiently sharp object is capable of cutting if it has a hardness sufficiently greater than the object being cut, and if it is applied with

    Cutting

    Cutting

    Cutting

  • Hearing loss
  • Partial or total inability to hear

    Wikimedia Commons has media related to Audiology. Hearing loss is either a partial inability to hear, or a total inability termed deafness. Hearing loss

    Hearing loss

    Hearing loss

    Hearing_loss

  • Cinnabar
  • Red mercury(II) sulfide mineral, HgS

    exhibits birefringence. Cinnabar has a mean refractive index near 3.2, a hardness between 2.0 and 2.5, and a specific gravity of approximately 8.1. The color

    Cinnabar

    Cinnabar

    Cinnabar

  • Diamond-like carbon
  • Class of amorphous carbon material

    bandgap range of 1.5 to 2.2 eV. The material demonstrated a hardness of 113 GPa on a Vickers hardness test vs diamonds rate at around 70 to 100 GPa. It was

    Diamond-like carbon

    Diamond-like carbon

    Diamond-like_carbon

  • Leeb rebound hardness test
  • Method of testing metal hardness

    The Leeb Rebound Hardness Test (LRHT) invented by Swiss company Proceq SA is one of the four most used methods for testing metal hardness. This portable

    Leeb rebound hardness test

    Leeb_rebound_hardness_test

  • Cabochon
  • Gemstone that has been shaped and polished

    for transparent stones. Hardness is also taken into account as softer gemstones with a hardness lower than 7 on the Mohs hardness scale are easily scratched

    Cabochon

    Cabochon

    Cabochon

  • Bipartite half
  • Graph whose nodes are one of the vertex sets of a bipartite graph

    In graph theory, the bipartite half or half-square of a bipartite graph G = (U,V,E) is a graph whose vertex set is one of the two sides of the bipartition

    Bipartite half

    Bipartite half

    Bipartite_half

  • Osmium
  • Chemical element with atomic number 76 (Os)

    electrical contacts, and other applications that require extreme durability and hardness. Osmium is a hard, brittle, blue-gray metal, and the densest stable element—about

    Osmium

    Osmium

    Osmium

  • Quadratically constrained quadratic program
  • Optimization problem in mathematics

    In mathematical optimization, a quadratically constrained quadratic program (QCQP) is an optimization problem in which both the objective function and

    Quadratically constrained quadratic program

    Quadratically_constrained_quadratic_program

  • Rolled homogeneous armour
  • Type of armour

    The typical Brinell Hardness range of MIL-A 12560 is 302-400 The MIL-12560K standard actually specifies four classes of hardnesses. The softest class I

    Rolled homogeneous armour

    Rolled_homogeneous_armour

  • Glock
  • Brand of polymer-framed semi-automatic pistols

    process produces a matte gray-colored, nonglare surface with a 64 Rockwell C hardness rating and a 99% resistance to salt water corrosion (which meets or exceeds

    Glock

    Glock

    Glock

  • Kickboxing
  • Full-contact hybrid martial art and combat sport

    Kickboxing A kickboxing match Focus punching, kicking, striking Hardness Full-contact Country of origin Ancient history, prehistoric Famous practitioners

    Kickboxing

    Kickboxing

    Kickboxing

  • Billiard ball
  • Ball used in cue sports

    specific game being played. Various particular ball properties such as hardness, friction coefficient, and resilience are important to accuracy. Early

    Billiard ball

    Billiard ball

    Billiard_ball

  • Johan August Brinell
  • Swedish metallurgist (1849–1925)

    creator of a method for quantifying the surface hardness of materials, now known as the Brinell hardness test. His name is also commemorated in the description

    Johan August Brinell

    Johan August Brinell

    Johan_August_Brinell

  • Persoz pendulum
  • A Persoz pendulum is a device used for measuring hardness of materials. The instrument consists of a pendulum which is free to swing on two balls resting

    Persoz pendulum

    Persoz pendulum

    Persoz_pendulum

  • Cubic zirconia
  • Cubic crystalline form of zirconium dioxide

    has no cleavage and exhibits a conchoidal fracture. Because of its high hardness, it is generally considered brittle. Under shortwave UV cubic zirconia

    Cubic zirconia

    Cubic zirconia

    Cubic_zirconia

  • Chromium
  • Chemical element with atomic number 24 (Cr)

    transition metal. Chromium is valued for its high corrosion resistance and hardness. A major development in steel production was the discovery that steel could

    Chromium

    Chromium

    Chromium

  • Tiger's eye
  • Chatoyant gemstone from the quartz family

    General Category Minerals Formula Silica (SiO2) Identification Colour golden to red-brown Mohs scale hardness 6.5–7 Luster Silky Specific gravity 2.64–2.71

    Tiger's eye

    Tiger's eye

    Tiger's_eye

  • High-entropy alloy
  • Alloys with high proportions of several metals

    Al1.3 film reached a maximum hardness of 8.74 GPa. As a result, the structural transition from FCC to BCC led to hardness enhancements with the increasing

    High-entropy alloy

    High-entropy alloy

    High-entropy_alloy

  • Cushion
  • Soft bag of ornamental material filled with soft material

    fragments. It may be used for sitting or kneeling upon, or to soften the hardness or angularity of a chair or couch. Decorative cushions often have a patterned

    Cushion

    Cushion

    Cushion

  • Punching bag
  • Type of exercise equipment

    bag is usually cylindrical and filled with various materials of suitable hardness. Punching bags have been used in martial arts and swordplay for the entire

    Punching bag

    Punching bag

    Punching_bag

  • Learning with errors
  • Mathematical problem in cryptography

    worst-case lattice problems. Subsequently, the LWE problem has been used as a hardness assumption to create public-key cryptosystems, such as the ring learning

    Learning with errors

    Learning_with_errors

  • Mechanical pencil
  • Pencil with a replaceable lead

    retracted inwards. Higher-end mechanical pencils often feature a lead hardness grade indicator and sometimes feature a retractable lead guide pipe. This

    Mechanical pencil

    Mechanical pencil

    Mechanical_pencil

  • Equihash
  • Memory-hard proof-of-work algorithm

    Equihash is a memory-hard Proof-of-work algorithm introduced by the University of Luxembourg's Interdisciplinary Centre for Security, Reliability and Trust

    Equihash

    Equihash

  • Rosiwal scale
  • Hardness scale in mineralogy

    The Rosiwal scale is a hardness scale in mineralogy, with its name given in memory of the Austrian geologist August Karl Rosiwal. The Rosiwal scale attempts

    Rosiwal scale

    Rosiwal_scale

  • Lignum vitae
  • Type of heavy and hard wood

    the Janka scale of hardness, which measures hardness of woods, lignum vitae ranks highest of the trade woods, with a Janka hardness of 4,390 lbf (19,500 N)

    Lignum vitae

    Lignum vitae

    Lignum_vitae

  • Chrysocolla
  • Phyllosilicate mineral

    Chrysocolla has a cyan (blue-green) color and is a minor ore of copper, having a hardness of 2.5 to 7.0. It is of secondary origin and forms in the oxidation zones

    Chrysocolla

    Chrysocolla

    Chrysocolla

  • Intersection non-emptiness problem
  • The intersection non-emptiness problem, also known as finite automaton intersection problem or the non-emptiness of intersection problem, is a PSPACE-complete

    Intersection non-emptiness problem

    Intersection_non-emptiness_problem

  • Genghis Khan
  • Khan of the Mongol Empire from 1206 to 1227

    suggests that the word "Genghis" bears connotations of strength, firmness, hardness, or righteousness. A third hypothesis proposes that the title is related

    Genghis Khan

    Genghis Khan

    Genghis_Khan

  • Vicat softening point
  • Determination of the softening point for materials that have no definite melting point

    Vicat softening temperature or Vicat hardness is the determination of the softening point for materials that have no definite melting point, such as plastics

    Vicat softening point

    Vicat softening point

    Vicat_softening_point

  • Topaz
  • Silicate mineral

    Lower quality topaz is commonly used as an abrasive material due to its hardness and it is used to produce refractory materials for high temperature environments

    Topaz

    Topaz

    Topaz

  • Heat treating
  • Process of heating something to alter it

    hardness either a range should be given or the minimum hardness specified. If a range is specified at least 5 points should be given. Only hardness is

    Heat treating

    Heat treating

    Heat_treating

  • Cricket
  • Team sport played with a bat and ball

    behind the batter) and the batters wear protective gear because of the hardness of the ball, which can be delivered at speeds of more than 145 kilometres

    Cricket

    Cricket

    Cricket

  • Ruby
  • Variety of corundum, mineral, gemstone

    which sold for US$34.8 million. Rubies have a hardness of 9.0 on the Mohs scale of mineral hardness. Among the natural gems, only moissanite and diamond

    Ruby

    Ruby

    Ruby

  • Carbonado
  • Impure form of polycrystalline diamond

    texture makes it more durable than a monocrystalline diamond. It is the same hardness as other types of diamond, but it is much tougher. Its polycrystalline

    Carbonado

    Carbonado

    Carbonado

  • Chrysoprase
  • Gemstone variety of chalcedony

    cap. As with all forms of chalcedony, chrysoprase has a hardness of 6 to 7 on the Mohs hardness scale and a conchoidal fracture like flint. The best known

    Chrysoprase

    Chrysoprase

    Chrysoprase

  • Strong NP-completeness
  • Computational property

    reduction is more restrictive than the usual poly-time reduction used for NP-hardness proofs. In particular, the pseudo-polynomial reduction cannot output a

    Strong NP-completeness

    Strong_NP-completeness

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