Logarithmic Hierarchy is the complexity class

Complexity class

In computational complexity theory, a complexity class is a set of problems of related resource-based complexity. A typical complexity class has a definition of the form:...

 of all computational problem

Computational problem

In theoretical computer science, a computational problem is a mathematical object representing a collection of questions that computers might want to solve. For example, the problem of factoring...

s solvable in a logarithmic

Logarithmic growth

In mathematics, logarithmic growth describes a phenomenon whose size or cost can be described as a logarithm function of some input. e.g. y = C log . Note that any logarithm base can be used, since one can be converted to another by a fixed constant...

 amount of computation time on an alternating Turing machine

Turing machine

A Turing machine is a theoretical device that manipulates symbols on a strip of tape according to a table of rules. Despite its simplicity, a Turing machine can be adapted to simulate the logic of any computer algorithm, and is particularly useful in explaining the functions of a CPU inside a...

 with a bounded number of alternation. It is a special case of hierarchy of bounded alternating Turing machine. It is equal to FO

FO (complexity)

FO is the complexity class of structures which can be recognised by formulae of first-order logic. It is the foundation of the field of descriptive complexity and is equal to the complexity class AC0 FO-regular...

 and to FO

FO (complexity)

FO is the complexity class of structures which can be recognised by formulae of first-order logic. It is the foundation of the field of descriptive complexity and is equal to the complexity class AC0 FO-regular...

-uniform AC0

AC0

AC0 is a complexity class used in circuit complexity. It is the smallest class in the AC hierarchy, and consists of all families of circuits of depth O and polynomial size, with unlimited-fanin AND gates and OR gates....

.

The th level of the Logarithmic Time Hierarchy is the set of languages recognised by alternating Turing machine in logtime with random access

Random-access Turing machine

In computational complexity, a field of computer science, random-access Turing machines are an extension of Turing machines used to speak about small complexity classes, especially for classes using logarithmic time, like DLOGTIME and the Logarithmic Hierarchy....

and alternation, beginning with existential state. LH is the union of all levels.