DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-09-02

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 EXP and NEXP

Definition

The exponential-time classes are $E X P : = ⋃_{k \geq 1} DTIME (2^{n^{k}}), N E X P : = ⋃_{k \geq 1} NTIME (2^{n^{k}}) .$

Remarks

The exponent $k$ is fixed per language, just as in the definition of $P$ and $N P$ .
The point is asymptotic growth: exponential time allows bounds of the form $2^{n^{k}}$ up to the usual multiplicative constants hidden in the class notation.

Depends on

The classes DTIME, NTIME, DSPACE, and NSPACE

Used by

NP ⊆ PSPACE ⊆ EXP Proposition

Dependency tree · two levels

3 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

Sanjeev Arora and Boaz Barak, Computational Complexity: A Modern Approach (standard reference, not scraped)