**Space Hierarchy Theorem**

In computational complexity theory, the **space hierarchy theorems** are separation results that show that both deterministic and nondeterministic machines can solve more problems in (asymptotically) more space, subject to certain conditions. For example, a deterministic Turing machine can solve more decision problems in space *n* log *n* than in space *n*. The somewhat weaker analogous theorems for time are the time hierarchy theorems.

The foundation for the hierarchy theorems lies in the intuition that with either more time or more space comes the ability to compute more functions (or decide more languages). The hierarchy theorems are used to demonstrate that the time and space complexity classes form a hierarchy where classes with tighter bounds contain fewer languages than those with more relaxed bounds. Here we define and prove the space hierarchy theorem.

The space hierarchy theorems rely on the concept of space-constructible functions. The deterministic and nondeterministic space hierarchy theorems state that for all space-constructible functions *f*(*n*),

- ,

where SPACE stands for either DSPACE or NSPACE.

Read more about Space Hierarchy Theorem: Statement, Proof, Comparison and Improvements, Refinement of Space Hierarchy

### Other articles related to "hierarchy":

... The priestly

**hierarchy**disappeared in the wake of the Spanish Conquest ... In this town, a

**hierarchy**of ‘mother-fathers’ is charged with the priestly tasks of prayer and sacrifice two of them on behalf of the town as a whole, fourteen for the wards, and three hundred for the ... Besides this

**hierarchy**, a large part of the population (about 10000) has been initiated as diviner (ajk’ij) ...

... to the Old Believers in 1846, thus establishing a full Church

**Hierarchy**of the Old Believers ... This

**hierarchy**became known as the Belokrinitskaya

**Hierarchy**...

... In the computational complexity theory, the low

**hierarchy**and high

**hierarchy**of complexity levels were introduced in 1983 by Uwe Schöning to describe the internal ... The low

**hierarchy**starts from complexity class P and grows "upwards", while the high

**hierarchy**starts from class NP and grows "downwards" ... On the other hand, if the low

**hierarchy**consists of at least two levels, then P is not NP ...

... in combinatorics on words is the Chomsky

**hierarchy**, developed by Noam Chomsky ... Chomsky's work is to divide language into four levels, or the language

**hierarchy**...

... Analytic

**Hierarchy**Process Hierarchical Decision Process Hierarchic Object-Oriented Design Hierarchical Bayes model Hierarchical clustering Hierarchical clustering of networks Hierarchical ...

### Famous quotes containing the words theorem, space and/or hierarchy:

“To insure the adoration of a *theorem* for any length of time, faith is not enough, a police force is needed as well.”

—Albert Camus (1913–1960)

“Our passionate preoccupation with the sky, the stars, and a God somewhere in outer *space* is a homing impulse. We are drawn back to where we came from.”

—Eric Hoffer (1902–1983)

“In a *hierarchy* every employee tends to rise to his level of incompetence.”

—Laurence J. Peter (1919–1990)