Concepts inDynamic ordered sets with exponential search trees
Binary search algorithm
In computer science, a binary search or half-interval search algorithm finds the position of a specified value (the input "key") within a sorted array. In each step, the algorithm compares the input key value with the key value of the middle element of the array. If the keys match, then a matching element has been found so its index, or position, is returned.
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Set (abstract data type)
In computer science, a set is an abstract data structure that can store certain values, without any particular order, and no repeated values. It is a computer implementation of the mathematical concept of a finite set. Unlike most other collection types, rather than retrieving a specific element from a set, one typically tests a value for membership in a set. Some set data structures are designed for static or frozen sets that do not change after they are constructed.
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Dynamical system
A dynamical system is a concept in mathematics where a fixed rule describes the time dependence of a point in a geometrical space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, and the number of fish each springtime in a lake. At any given time a dynamical system has a state given by a set of real numbers that can be represented by a point in an appropriate state space.
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String searching algorithm
In computer science, string searching algorithms, sometimes called string matching algorithms, are an important class of string algorithms that try to find a place where one or several strings are found within a larger string or text. Let ¿ be an alphabet. Formally, both the pattern and searched text are vectors of elements of ¿. The ¿ may be a usual human alphabet (for example, the letters A through Z in the Latin alphabet).
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PSPACE
In computational complexity theory, PSPACE is the set of all decision problems which can be solved by a Turing machine using a polynomial amount of space.
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Partially ordered set
In mathematics, especially order theory, a partially ordered set (or poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set. A poset consists of a set together with a binary relation that indicates that, for certain pairs of elements in the set, one of the elements precedes the other.
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Square root
In mathematics, a square root of a number a is a number y such that y = a, or, in other words, a number y whose square (the result of multiplying the number by itself, or y × y) is a. For example, 4 is a square root of 16 because 4 = 16. Every non-negative real number a has a unique non-negative square root, called the principal square root, which is denoted by, where ¿ is called radical sign. For example, the principal square root of 9 is 3, denoted, because {{{1}}} and 3 is non-negative.
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