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Exponential functions with bases 2 and 1/2. The exponential function is a mathematical function denoted by () = or (where the argument x is written as an exponent).Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, although it can be extended to the complex numbers or generalized to other mathematical objects like matrices or Lie algebras.
2-EXPTIME. In computational complexity theory, the complexity class 2-EXPTIME (sometimes called 2-EXP) is the set of all decision problems solvable by a deterministic Turing machine in O (2 2p(n)) time, where p ( n) is a polynomial function of n . In terms of DTIME ,
EXPTIME. In computational complexity theory, the complexity class EXPTIME (sometimes called EXP or DEXPTIME) is the set of all decision problems that are solvable by a deterministic Turing machine in exponential time, i.e., in O (2 p(n)) time, where p (n) is a polynomial function of n. EXPTIME is one intuitive class in an exponential hierarchy ...
Characterisation 3 involves defining the natural logarithm before the exponential function is defined. First, This means that the natural logarithm of equals the (signed) area under the graph of between and . If , then this area is taken to be negative. Then, is defined as the inverse of , meaning that by the definition of an inverse function.
An exponential-Golomb code (or just Exp-Golomb code) is a type of universal code. To encode any nonnegative integer x using the exp-Golomb code: Count the bits written, subtract one, and write that number of starting zero bits preceding the previous bit string. The first few values of the code are: 0 ⇒ 1 ⇒ 1. 1 ⇒ 10 ⇒ 010.
Power of two. A power of two is a number of the form 2n where n is an integer, that is, the result of exponentiation with number two as the base and integer n as the exponent. Powers of two with non-negative exponents are integers: 20 = 1, 21 = 2, and 2n is two multiplied by itself n times. [1][2] The first ten powers of 2 for non-negative ...
Exponential hierarchy. In computational complexity theory, the exponential hierarchy is a hierarchy of complexity classes that is an exponential time analogue of the polynomial hierarchy. As elsewhere in complexity theory, “exponential” is used in two different meanings (linear exponential bounds for a constant c, and full exponential ...
x 1 = x; x 2 = x 2 for i = k - 2 to 0 do if n i = 0 then x 2 = x 1 * x 2; x 1 = x 1 2 else x 1 = x 1 * x 2; x 2 = x 2 2 return x 1. The algorithm performs a fixed sequence of operations (up to log n): a multiplication and squaring takes place for each bit in the exponent, regardless of the bit's specific value. A similar algorithm for ...