Space Hierarchy Theorem - Statement

Statement

Formally, a function is space-constructible if and there exists a Turing machine which computes the function in space when starting with an input, where represents a string of s. Most of the common functions that we work with are space-constructible, including polynomials, exponents, and logarithms.

For every space-constructible function f:\mathbb{N} \longrightarrow
\mathbb{N}, there exists a language that is decidable in space but not in space .

Read more about this topic:  Space Hierarchy Theorem

Famous quotes containing the word statement:

    After the first powerful plain manifesto
    The black statement of pistons, without more fuss
    But gliding like a queen, she leaves the station.
    Stephen Spender (1909–1995)

    Eroticism has its own moral justification because it says that pleasure is enough for me; it is a statement of the individual’s sovereignty.
    Mario Vargas Llosa (b. 1936)

    It is commonplace that a problem stated is well on its way to solution, for statement of the nature of a problem signifies that the underlying quality is being transformed into determinate distinctions of terms and relations or has become an object of articulate thought.
    John Dewey (1859–1952)