In computational complexity theory, DLOGTIME is the complexity class of all computational problems solvable in a logarithmic amount of computation time on a deterministic Turing machine. It must be defined on a random-access Turing machine, since otherwise the input tape is longer than the range of cells that can be accessed by the machine. It is a very weak model of time complexity: no random-access Turing machine with a smaller deterministic time bound can access the whole input.[1]
^Johnson, David S. (1990), "A catalog of complexity classes", Handbook of theoretical computer science, Vol. A, Elsevier, Amsterdam, pp. 67–161, MR 1127168. See in particular p. 140.
In computational complexity theory, DLOGTIME is the complexity class of all computational problems solvable in a logarithmic amount of computation time...
Amortized time per operation using a bounded priority queue logarithmic time DLOGTIME O ( log n ) {\displaystyle O(\log n)} log n {\displaystyle \log n}...
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}}...
contains every unary language. From a descriptive complexity viewpoint, DLOGTIME-uniform AC0 is equal to the descriptive class FO+BIT of all languages describable...
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...
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...
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