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.
The class IP
Definition
The class consists of languages having an interactive protocol with a probabilistic polynomial-time verifier (Probabilistic polynomial-time Turing machines), polynomially bounded interaction, completeness at least , and soundness at most in the sense of Completeness and soundness of an interactive protocol. Equivalent constant gaps follow by sequential repetition.
Depends on
Used by
- Private-coin, public-coin, and Arthur--Merlin protocols Definition
- NP is contained in IP Proposition
- Graph nonisomorphism is in IP Theorem
- IP is contained in PSPACE Theorem
Dependency tree · two levels
2 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, Definition 8.5 (standard reference, not scraped)