Alphabeta Math
DefinitionDefinition: Literature-sourcedProof: Not applicableaudited 2026-09-12
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 GNFA state-elimination update

Definition

Let G=(Q,Σ,s,t,λ) be a GNFA, and let r∈Q∖{s,t} be an interior state. The state-elimination update removes r and keeps the surviving state set Q′:=Q∖{r}.

For surviving states p,q∈Q′, the new label is λ′(p,q):=λ(p,q)+λ(p,r)(λ(r,r))∗λ(r,q).

The resulting GNFA G∖r has the same distinguished start and accept states s,t, the surviving state set Q′, and the label function λ′.

Remarks

  • The first summand keeps the old direct p-to-q behavior.

  • The second summand records paths that enter r, loop there any finite number of times, and then leave for q.

Depends on

Used by

Dependency tree · two levels

8 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