DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-5.6-terra)audited 2026-09-06

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

The classes L and NL

Definition

For a function $s$ , let $N W O R K S P A C E (s (n))$ denote the languages decided by nondeterministic read-only-input machines using $O (s (n))$ work cells. Thus $L : = D W O R K S P A C E (\log_{2} (n + 2)), N L : = N W O R K S P A C E (\log_{2} (n + 2)) .$ Here $D W O R K S P A C E$ is exactly the local uncharged-input class of Read-only-input work-space classes and constructibility. The names L and NL below never silently mean the library's all-tapes $D S P A C E$ and $N S P A C E$ .

Depends on

Used by

A logspace-uniform Boolean circuit family Definition
NL equals coNL follows by swapping accepting and rejecting states False statement
A reachable-vertex count is verifiable in NL Lemma
Logspace reductions compose Lemma
Directed s-t connectivity is NL-complete Theorem
Immerman-Szelepcsényi theorem: NL equals coNL Theorem
NL is contained in read-only-input DWORKSPACE(log-squared n) Theorem

Dependency tree · two levels

4 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

Arora and Barak, Computational Complexity, Definition 3.5 (standard reference, not scraped)