Concepts inAmplifying lower bounds by means of self-reducibility
Computational problem
In theoretical computer science, a computational problem is a mathematical object representing a collection of questions that computers might want to solve. For example, the problem of factoring "Given a positive integer n, find a nontrivial prime factor of n. " is a computational problem. Computational problems are one of the main objects of study in theoretical computer science. The field of algorithms studies methods of solving computational problems efficiently.
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Alexander Razborov
Aleksandr Aleksandrovich Razborov (Russian: Алекса́ндр Алекса́ндрович Разбо́ров; born February 16, 1963), sometimes known as Sasha Razborov, is a Soviet and Russian mathematician and computational theorist who won the Nevanlinna Prize in 1990 for introducing the "approximation method" in proving Boolean circuit lower bounds of some essential algorithmic problems, and the Gödel Prize with Steven Rudich in 2007 for their paper "Natural Proofs. " His advisor was Sergei Adian.
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Random self-reducibility
Random self-reducibility (RSR) is the rule that a good algorithm for the average case implies a good algorithm for the worst case. RSR is the ability to solve all instances of a problem by solving a large fraction of the instances.
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Asymptotic analysis
In mathematical analysis, asymptotic analysis is a method of describing limiting behavior. The methodology has applications across science. Examples are in computer science in the analysis of algorithms, considering the performance of algorithms when applied to very large input datasets. the behavior of physical systems when they are very large. in accident analysis when identifying the causation of crash through count modeling with large number of crash counts in a given time and space.
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Space–time tradeoff
In computer science, a space–time or time–memory tradeoff is a situation where the memory use can be reduced at the cost of slower program execution (and, conversely, the computation time can be reduced at the cost of increased memory use).
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If and only if
↔ ⇔ ≡ Logical symbolsrepresenting iff In logic and related fields such as mathematics and philosophy, if and only if (shortened iff) is a biconditional logical connective between statements. In that it is biconditional, the connective can be likened to the standard material conditional ("only if," equal to "if ... then") combined with its reverse ("if"); hence the name. The result is that the truth of either one of the connected statements requires the truth of the other, i.e.
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Counting
Counting is the action of finding the number of elements of a finite set of objects.
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Algorithm
In mathematics and computer science, an algorithm Listen/ˈælɡərɪðəm/ (originating from al-Khwārizmī, the famous mathematician Muḥammad ibn Mūsā al-Khwārizmī) is a step-by-step procedure for calculations. Algorithms are used for calculation, data processing, and automated reasoning. More precisely, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function.
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