IP ⊆ SZK
Statement
Migrated verbatim from zero-knowledge-proof § Other results:
Notes
class: unstated: no citing page says which notion of reduction is meant.
Recording a class the wiki does not state would add a claim.
class: free because a containment between complexity classes is proved
by any argument at all; the reduction-class axis does not discriminate
here, and unstated would wrongly suggest the information is missing.
Recorded during migration and not fixed — these are claims about the source text, not changes to it:
- SUSPECTED MATHEMATICAL ERROR (reported, not fixed): as written this says IP = PSPACE is contained in SZK. But SZK is contained in AM \cap coAM, so SZK = PSPACE would collapse the polynomial hierarchy. The actual BGG+90 result is that every language in IP has a COMPUTATIONAL zero-knowledge proof ASSUMING one-way functions exist (with statistical/perfect ZK obtained only in the multi-prover or argument settings). The bullet drops the OWF hypothesis AND upgrades computational ZK to statistical ZK.
- Consequently the hypothesis set is also wrong: the real edge is conjunctive {interactive-proof-systems, hash-function(OWF)} ⇒ computational-zero-knowledge (content/Complexity/computational-zero-knowledge.md exists).
- This is the single most serious claim-level defect found in this chunk; the page is status: stub and its .fact-check queue entry should be checked.