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:

    “Eloquence must be grounded on the plainest narrative. Afterwards, it may warm itself until it exhales symbols of every kind and color, speaks only through the most poetic forms; but first and last, it must still be at bottom a biblical statement of fact.”
    —Ralph Waldo Emerson (1803–1882)

    “No statement about God is simply, literally true. God is far more than can be measured, described, defined in ordinary language, or pinned down to any particular happening.”
    —David Jenkins (b. 1925)

    “The honor my country shall never be stained by an apology from me for the statement of truth and the performance of duty; nor can I give any explanation of my official acts except such as is due to integrity and justice and consistent with the principles on which our institutions have been framed.”
    —Andrew Jackson (1767–1845)