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Padding Argument
In computational complexity theory, the padding argument is a tool to conditionally prove that if some complexity classes are equal, then some other bigger classes are also equal. Example The proof that P (complexity), P = NP (complexity), NP implies EXP = NEXP uses "padding". \mathrm \subseteq \mathrm by definition, so it suffices to show \mathrm \subseteq \mathrm. Let ''L'' be a language in NEXP. Since ''L'' is in NEXP, there is a non-deterministic Turing machine ''M'' that decides ''L'' in time 2^ for some constant ''c''. Let : L'=\, where '1' is a symbol not occurring in ''L''. First we show that L' is in NP, then we will use the deterministic polynomial time machine given by P = NP to show that ''L'' is in EXP. L' can be Decision problem, decided in non-deterministic polynomial time as follows. Given input x', verify that it has the form x' = x1^ and reject if it does not. If it has the correct form, simulate ''M''(''x''). The simu ... [...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 explores the relationships between these classifications. 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 logic gate, gates in a circuit (used in circuit complexity) and the number of processors (used in parallel computing). O ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
