computational complexity In computer science, the computational complexity or simply complexity of an algorithm is the amount of resources required to run it. Particular focus is given to computation time (generally measured by the number of needed elementary operations) ...

, a field of

computer science Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to practical disciplines (includin ...

, random-access Turing machines are an extension of

Turing machine A Turing machine is a mathematical model of computation describing an abstract machine that manipulates symbols on a strip of tape according to a table of rules. Despite the model's simplicity, it is capable of implementing any computer algor ...

s used to speak about small complexity classes, especially for classes using logarithmic

time Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future. It is a component quantity of various measurements used to sequence events, t ...

, like

DLOGTIME 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 o ...

and the logarithmic hierarchy.

Definition

On a random-access Turing machine, there is a special ''

pointer Pointer may refer to: Places * Pointer, Kentucky * Pointers, New Jersey * Pointers Airport, Wasco County, Oregon, United States * The Pointers, a pair of rocks off Antarctica People with the name * Pointer (surname), a surname (including a list ...

'' tape of logarithmic space accepting a binary vocabulary. The Turing machine has a special state such that when the binary number on the ''pointer'' tape is 'p', the Turing machine will write on the working tape the ''p''th symbol of the input. The pointer tape facility lets the Turing machine read any letter of the input without taking time to move over the entire input. This is mandatory for complexity classes using less than

linear time In computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations performed by t ...

References

Neil Immerman Neil Immerman (born 24 November 1953, Manhasset, New York) is an American theoretical computer scientist, a professor of computer science at the University of Massachusetts Amherst.

Descriptive Complexity ''Descriptive Complexity'' is a book in mathematical logic and computational complexity theory by Neil Immerman. It concerns descriptive complexity theory, an area in which the expressibility of mathematical properties using different types of log ...

'' (1999 Springer), chapter 5 Complexity classes {{Comp-sci-theory-stub