DLOGTIME

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DLOGTIME is the complexity class of all computational problems solvable in a logarithmic amount of computation time on a deterministic Turing machine. It is the smallest nontrivial class using the resource of deterministic time.^{[citation needed]} It must be defined on a random-access Turing machine, since otherwise the machine does not have time to read the entire input tape.

DLOGTIME-uniformity is important in circuit complexity.

The problem of testing the length of the input string can be solved in DLOGTIME, by binary searching for possible input sizes.

v t e Important complexity classes (more)

Considered feasible	DLOGTIME AC⁰ ACC⁰ TC⁰ L SL RL NL NC SC CC P P-complete ZPP RP BPP BQP

Suspected infeasible	UP NP NP-complete NP-hard co-NP co-NP-complete AM PH ⊕P PP #P #P-complete IP PSPACE PSPACE-complete

Considered infeasible	EXPTIME NEXPTIME EXPSPACE ELEMENTARY PR R RE ALL

Class hierarchies	Polynomial hierarchy Exponential hierarchy Grzegorczyk hierarchy Arithmetical hierarchy Boolean hierarchy

Families of classes	DTIME NTIME DSPACE NSPACE Probabilistically checkable proof Interactive proof system

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