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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.
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 2 p(n)) time, where p(n) is a polynomial function of n.
EXPTIME is one intuitive class in an exponential hierarchy of complexity classes with increasingly more complex oracles or quantifier alternations. For example, the class 2-EXPTIME is defined similarly to EXPTIME but with a doubly exponential time bound. This can be generalized to higher and higher time bounds.
Can the fast Fourier transform be computed in o(n log n) time? What is the fastest algorithm for multiplication of two n-digit numbers? What is the lowest possible average-case time complexity of Shellsort with a deterministic fixed gap sequence? Can 3SUM be solved in strongly sub-quadratic time, that is, in time O(n 2−ϵ) for some ϵ>0?
Codon is a language with an ahead-of-time (AOT) compiler, that (AOT) compiles a statically-typed Python-like language with "syntax and semantics are nearly identical to Python's, there are some notable differences" [149] e.g. it uses 64-bit machine integers, for speed, not arbitrary like Python, and it claims speedups over CPython are usually ...
The time complexity of an algorithm counts the number of arithmetic operations sufficient for the algorithm to solve the problem. For example, Gaussian elimination requires on the order of D 3 operations, and so it is said to have polynomial time-complexity, because its complexity is bounded by a cubic polynomial. There are examples of ...
The worst-case time complexity of Shellsort is an open problem and depends on the gap sequence used, with known complexities ranging from O(n 2) to O(n 4/3) and Θ(n log 2 n).
Ye and Tse [7] present a polynomial-time algorithm, which extends Karmarkar's algorithm from linear programming to convex quadratic programming. On a system with n variables and L input bits, their algorithm requires O(L n) iterations, each of which can be done using O(L n 3) arithmetic operations, for a total runtime complexity of O(L 2 n 4).