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CorollaryStatement: Literature-sourcedProof: AI-generatedPipeline-generatedprecheck passjudge pass (gpt-5.6-terra)audited 2026-09-06
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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.

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Read-only-input nondeterministic work space is closed under complement above logarithmic space

Statement

If s is work-space constructible and log⁡2(n+2)=O(s(n)), then NWORKSPACE(s(n))=coNWORKSPACE(s(n)). This is the read-only-input work-space notation introduced on this page, not an unqualified assertion about the library's all-tapes NSPACE convention.

Facts & Assumptions

Given: a work-space-constructible s satisfying log⁡2(n+2)=O(s(n)).

[L1]

The general read-only-input NWORKSPACE(s) complement equality is established by the Immerman--Szelepcsényi theorem (Immerman-Szelepcsényi theorem: NL equals coNL).

Proof

technique · direct extraction
1.1

The hypotheses here are exactly the hypotheses of the general clause in [L1].

L1given
2.1

Applying that clause gives NWORKSPACE(s(n))=coNWORKSPACE(s(n)), which is closure under complement.

L1step 1.1∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

5 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