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It is in EXPTIME because a trivial simulation requires O(k) time, and the input k is encoded using O(log k) bits which causes exponential number of simulations. It is EXPTIME-complete because, roughly speaking, we can use it to determine if a machine solving an EXPTIME problem accepts in an exponential number of steps; it will not use more. [4]
An algorithm is said to be exponential time, if T(n) is upper bounded by 2 poly(n), where poly(n) is some polynomial in n. More formally, an algorithm is exponential time if T(n) is bounded by O(2 n k) for some constant k. Problems which admit exponential time algorithms on a deterministic Turing machine form the complexity class known as EXP.
Exponential functions with bases 2 and 1/2. In mathematics, the exponential function is the unique real function which maps zero to one and has a derivative equal to its value. . The exponential of a variable is denoted or , with the two notations used interchangeab
The exponential time hypothesis also implies that it is not possible to solve the k-SUM problem (given real numbers, find of them that add to zero) in time (). The strong exponential time hypothesis implies that it is not possible to find k {\displaystyle k} -vertex dominating sets more quickly than in time n k − o ( 1 ) {\displaystyle n^{k-o ...
The definition of e x as the exponential function allows defining b x for every positive real numbers b, in terms of exponential and logarithm function. Specifically, the fact that the natural logarithm ln(x) is the inverse of the exponential function e x means that one has = () = for every b > 0.
The elementary functions are constructed by composing arithmetic operations, the exponential function (), the natural logarithm (), trigonometric functions (,), and their inverses. The complexity of an elementary function is equivalent to that of its inverse, since all elementary functions are analytic and hence invertible by means of Newton's ...
Although the P = NP problem itself remains open despite a million-dollar prize and a huge amount of dedicated research, efforts to solve the problem have led to several new techniques. In particular, some of the most fruitful research related to the P = NP problem has been in showing that existing proof techniques are insufficient for answering ...
An example of an EXPSPACE-complete problem is the problem of recognizing whether two regular expressions represent different languages, where the expressions are limited to four operators: union, concatenation, the Kleene star (zero or more copies of an expression), and squaring (two copies of an expression).
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