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Logarithm

Description

The class of decision problems solvable by a deterministic Turing machine restricted to memory usage that is logarithmic in the size of the input.

Space constraint

$\!$\*FormBox[RowBox[{RowBox[{"S", "(", "n", ")"}], " ", "=", " ", RowBox[{"O", "(", RowBox[{"log", " ", "n"}], ")"}]}], TraditionalForm]$ (on a deterministic turing machine)$

Canonical problems

undirected connectivity | ...

Complete problems

cycle existance | directed deterministic graph reachability | ...

Related classes

open problems | L ≟ P | L ≟ NL
equalities |

Best supersets

L ⊆ intersection _coR_HL | L ⊆ intersection _coUL | L ⊆ R_HL | L ⊆ UL

Best subsets

L ⊇ NC^1 | L ⊇ PBP

Oracle superset separations

Oracle subset separations

Class inclusions diagram

(supersets shown above subsets)

Other properties

L is used to model computations where the input size exceeds available random-access memory.

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