Alphabeta MathHow 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.
Oracle Turing machines
Definition
An oracle Turing machine is a finite Turing-machine program with, in addition to its ordinary instructions, a query instruction: on a query number , it receives the bit exactly when , where is its oracle. Write when its run on halts with output . Thus even with an infinite oracle, each halting run has only finitely many transitions and queries.
Remarks
This is the membership-query presentation of the oracle computations in Relative computability and relative enumerability.
Depends on
Used by
- Tagged join of oracles Definition
- The Turing jump Definition
- Truth-table reduction Definition
- Turing reducibility and equivalence Definition
- An oracle machine reads the infinite oracle at once False statement
- Every oracle is strictly below its jump Theorem
Dependency tree · one level
1 result within one dependency step 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
- Ludovic Patey, Computability Theory, §4.2 (standard reference, not scraped)
- Sebastiaan Terwijn, Computability Theory, §5.1 (standard reference, not scraped)