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DLOGTIME

DLOGTIME

In computational complexity theory, DLOGTIME is the complexity class of all computational problems solvable in a logarithmic amount of computation time

DLOGTIME

Time complexity

Estimate of time taken for running an algorithm

Amortized time per operation using a bounded priority queue logarithmic time DLOGTIME O ( log ⁡ n ) {\displaystyle O(\log n)} log ⁡ n {\displaystyle \log n}

Time complexity

Time_complexity

Oracle machine

Abstract machine used to study decision problems

with respect to polynomial time reductions, PSAT=PNP. However, if A = DLOGTIME, then ASAT may not equal ANP. (The definition of A B {\displaystyle A^{B}}

Oracle machine

Oracle_machine

Circuit complexity

Model of computational complexity

the circuit family is said to be P-uniform. The stricter requirement of DLOGTIME-uniformity is of particular interest in the study of shallow-depth circuit-classes

Circuit complexity

Circuit_complexity

Complexity class used in circuit complexity

{\displaystyle {\mathsf {TC}}^{0}} , while DLOGTIME is suspected to be equivalent in strength in some sense, DLOGTIME-uniformity is usually assumed, when uniformity

TC0

NC (complexity)

Class in computational complexity theory

width 4 or less. This is true for both the uniform and nonuniform case (DLOGTIME-uniformity suffices). One can relate the NC classes to the space classes

NC (complexity)

NC_(complexity)

P-complete

Class in computational complexity theory

reduction, such as uniform A C 0 {\displaystyle AC^{0}} many-one reductions, DLOGTIME reductions, or polylogarithmic projections. In order to prove that a given

P-complete

Complexity class of bounded-depth circuits

contains every unary language. From a descriptive complexity viewpoint, DLOGTIME-uniform AC0 is equal to the descriptive class FO+BIT of all languages describable

AC0

BIT predicate

Test of a specified bit in a binary number

multiplication predicates. It is also the same as the circuit complexity class DLOGTIME-uniform AC0. Here, AC0 describes the problems that can be computed by circuits

BIT predicate

BIT_predicate