No reduction from MIP to Multi-prover extensions
A reduction of class unstated from MIP to Multi-prover extensions would imply a contradiction.
Statement
Migrated verbatim from quantum-interactive-proofs § Multi-prover extensions:
- vs : the classical multi-prover class , so entanglement exponentially (in fact, incomparably) increases prover power.
Notes
source: folklore: the claim carried no citation on the page it was
migrated from, and none was invented.
class: unstated: no citing page says which notion of reduction is meant.
Recording a class the wiki does not state would add a claim.
Recorded during migration and not fixed — these are claims about the source text, not changes to it:
- Derived by combining MIP = NEXP here with MIP* = RE at line 28, not stated as a theorem, and nothing marks it as derived.
- TYPING LOSS: the bare pair {MIP} ⇒ {MIP*} is indistinguishable from a plain inclusion.
- The page’s gloss ‘exponentially (in fact, incomparably) increases prover power’ is imprecise and half-corrects itself in the same sentence: RE versus NEXP is not an exponential gap.
- Uncited.
- MISSING CITATION for MIP = NEXP (Babai-Fortnow-Lund 1991).
- Composite: the theorem MIP = NEXP plus the derived separation MIP ⊊ MIP* (obtained by combining with MIP* = RE on line 28).
- ‘exponentially (in fact, incomparably) increases prover power’ is imprecise: RE vs NEXP is not an ‘exponential’ gap, and the parenthetical half-corrects the first half in the same sentence.
- MIP, NEXP have no wiki pages.