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Compression Theorem
In computational complexity theory, the compression theorem is an important theorem about the Computational complexity, complexity of computable functions. The theorem states that there exists no largest complexity class, with computable boundary, which contains all computable functions. Compression theorem Given a Gödel numbering \varphi of the computable functions and a Blum complexity measure \Phi where a complexity class for a boundary function f is defined as :\mathrm(f):= \. Then there exists a total computable function f so that for all i :\mathrm(\varphi_i) = \mathrm(\varphi_) and :\mathrm(\varphi_i) \subsetneq \mathrm(\varphi_). References *. *. Computational complexity theory Structural complexity theory Theorems in the foundations of mathematics {{Comp-sci-theory-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Complexity Theory
In theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and relating these classes to each other. A computational problem is a task solved by a computer. A computation problem is solvable by mechanical application of mathematical steps, such as an algorithm. A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used. The theory formalizes this intuition, by introducing mathematical models of computation to study these problems and quantifying their computational complexity, i.e., the amount of resources needed to solve them, such as time and storage. Other measures of complexity are also used, such as the amount of communication (used in communication complexity), the number of gates in a circuit (used in circuit complexity) and the number of processors (used in parallel computing). One of the roles of compu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
