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
NP-hardness nor "Undecidable". For instance, the language of True quantified Boolean formulas is decidable in polynomial space, but not in non-deterministic polynomial time (unless NP = PSPACE). NP-hard problems do not have to be elements of the complexity class NP. As NP plays a central role in computational complexity, it is used as the basis of several classes: NP-hard problems are often tackled with rules-based languages in areas including: NP-hardness NP-hardness (non-deterministic polynomial-time hardness), in computational complexity theory, is the defining property of a class of problems that are, informally, "at least as hard as the hardest problems in NP". A