In modern companies, overlapping hierarchies often slow down decision-making more than technical limitations.

The rigid hierarchy in the ministry made reform slow and contentious.

The company's hierarchial structure made decision-making slow and rigid.

Researchers compared different arithmetical hierarchies to better understand the limits of computable functions.

Researchers studying computability often compare different arithmetic hierarchies to understand the relative complexity of decision problems.

Graduate students compared various Chomsky hierarchies to determine their relative expressive power.

Marketing researchers compared different hierarchies of effects to determine which model best predicted consumer behavior.

Researchers often analyze the arithmetic hierarchy to understand the complexity of definable sets.

To determine the descriptive power of different fragments, researchers examine the arithmetical hierarchy, which classifies the complexity of first-order formulas and the sets they define by counting alternations between blocks of unbounded existential and universal quantifiers.

Students studying formal language theory often begin by learning the Chomsky hierarchy to understand how grammar classes relate.