Sentence examples for hierarchy of complexity from inspiring English sources

Proposition 3.1 provides the basis for defining a hierarchy of complexity classes – i.e. the so-called Polynomial Hierarchy [\ \textbf{PH}\)] – based on the logical representation of computational problems.

Even taking into account our current inability to resolve Open Questions 1 3, the hierarchy of complexity classes depicted in Figure 2 ranging from \ \textbf{P}\) to \ \textbf{EXP}\) represent the most robust benchmarks of computational difficulty now available.

The antiviral landscape can be viewed as a hierarchy of complexity, beginning at the whole organism level and progressing downward to isolated tissues, populations of cells, and single cells.

3.4.3 Parallel, probabilistic, and quantum complexity Even taking into account our current inability to resolve Open Questions 1 3, the hierarchy of complexity classes depicted in Figure 2 ranging from \ \textbf{P}\) to \ \textbf{EXP}\) represent the most robust benchmarks of computational difficulty now available.

The hierarchy of complexity started with a first level of values relevant to family and self, followed by a second level with reference to the peer-group of a person, and reached the third level with values related to mankind (Fig. 1, Table 1).

The models formed a nested hierarchy of complexity for model testing, comparing the free ratio to two ratio and both to the one ratio (for cases where the two ratio was not supported but the free ratio was), with p-values calculated from a χ distribution.

The projective sets form a hierarchy of increasing complexity.

We shall discuss the hierarchy of statement complexity in more detail in the next section.

In such work, Brookner materializes the French philosopher Teilhard de Chardin who saw nature assuming a succession of higher and higher forms of organization, partaking in a hierarchy of increasing complexity from subatomic particles, through atoms, molecules, proteins, cells, organisms, humans, and ultimately to God, or a supreme and omniscient power.

At the very least, this depiction recognizes potential barriers to achieving veritable restoration in relation to the requirements of rehabilitating landscape hierarchies of increasing complexity (e.g. biodiversity interactions < biodiversity assemblages < nutrient and/or hydrological cycles < landform assemblages < geology and climate).

Deviation from the historical system increases (from small to large to irreversible) as increassing hierarchies of landscape complexity are crossed, resulting in commensurate increases in management input (from modest to intensive to prohibitive) required for re-instatement of the historical system.