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

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