Hardness Hardness Hardness is a measure of the resistance to localized plastic deformation induced by either mechanical indentation or abrasion. Some materials (e.g. metals) are harder than others (e.g. plastics, wood). Macroscopic hardness is generally characterized by strong intermolecular bonds, but the behavior of solid materials under force is complex; therefore, there are different measurements of hardness: "scratch hardness", "indentation hardness", and "rebound hardness". Hardness is dependent on ductility, elastic stiffness, plasticity, strain, strength, toughness, viscoelasticity, and viscosity. Common examples of hard matter are ceramics, concrete, certain metals, and superhard materials, which can be contrasted with soft matter. There are three
Computational hardness assumption which is a computational hardness assumption about random instances of 3-SAT (sampled to maintain a specific ratio of clauses to variables). Average-case computational hardness assumptions are useful for proving average-case hardness in applications like statistics, where there is a natural distribution over inputs. Additionally, the planted clique hardness assumption has also been used to distinguish between polynomial and quasi-polynomial worst-case time complexity of other problems, similarly to the Exponential Time Hypothesis. The Unique Label Cover problem is a constraint satisfaction problem, where each constraint formula_60 involves two variables formula_77, and for each value of formula_26 there is a "unique" value