Interactive Proofs Lecture 16 What the all-powerful can convince - PowerPoint PPT Presentation

Arthur Merlin Proofs Arthur-Merlin proof-systems Arthur: polynomial time verifier 10

Arthur Merlin Proofs Arthur-Merlin proof-systems Arthur: polynomial time verifier Merlin: unbounded prover 10

Arthur Merlin Proofs Arthur-Merlin proof-systems Arthur: polynomial time verifier Merlin: unbounded prover Random coins come from a beacon 10

Arthur Merlin Proofs Arthur-Merlin proof-systems Arthur: polynomial time verifier Merlin: unbounded prover Random coins come from a beacon Public coin proof-system 10

Arthur Merlin Proofs Arthur-Merlin proof-systems Arthur: polynomial time verifier Merlin: unbounded prover Random coins come from a beacon Public coin proof-system Arthur sends no messages nor flips any coins 10

MA and AM 11

MA and AM Class of languages with two message Arthur-Merlin protocols 11

MA and AM Class of languages with two message Arthur-Merlin protocols AM (or AM[2]): One message from beacon, followed by one message from Merlin 11

MA and AM Class of languages with two message Arthur-Merlin protocols AM (or AM[2]): One message from beacon, followed by one message from Merlin MA (or MA[2]): One message from Merlin followed by one message from beacon 11

MA and AM Class of languages with two message Arthur-Merlin protocols AM (or AM[2]): One message from beacon, followed by one message from Merlin MA (or MA[2]): One message from Merlin followed by one message from beacon Contain NP and BPP 11

Multiple-message proofs 12

Multiple-message proofs AM[k], MA[k], IP[k]: k(n) messages 12

Multiple-message proofs AM[k], MA[k], IP[k]: k(n) messages Turns out IP[k] ⊆ AM[k+2]! 12

Multiple-message proofs AM[k], MA[k], IP[k]: k(n) messages Turns out IP[k] ⊆ AM[k+2]! Turns out IP[const] = AM[const] = AM[2]! 12

Multiple-message proofs AM[k], MA[k], IP[k]: k(n) messages Turns out IP[k] ⊆ AM[k+2]! Turns out IP[const] = AM[const] = AM[2]! Called AM 12

Multiple-message proofs AM[k], MA[k], IP[k]: k(n) messages Turns out IP[k] ⊆ AM[k+2]! Turns out IP[const] = AM[const] = AM[2]! Called AM Turns out IP[poly] = AM[poly] = PSPACE! 12

Multiple-message proofs AM[k], MA[k], IP[k]: k(n) messages Turns out IP[k] ⊆ AM[k+2]! Turns out IP[const] = AM[const] = AM[2]! Called AM Turns out IP[poly] = AM[poly] = PSPACE! Called IP (= PSPACE) 12

Multiple-message proofs AM[k], MA[k], IP[k]: k(n) messages Turns out IP[k] ⊆ AM[k+2]! Turns out IP[const] = AM[const] = AM[2]! Called AM Turns out IP[poly] = AM[poly] = PSPACE! Called IP (= PSPACE) Later. 12

How can private coins be avoided? 13

How can private coins be avoided? Example: GNI 13

How can private coins be avoided? Example: GNI Recall GNI protocol used private coins 13

How can private coins be avoided? Example: GNI Recall GNI protocol used private coins An alternate view of GNI 13

How can private coins be avoided? Example: GNI Recall GNI protocol used private coins An alternate view of GNI Each of G 0 and G 1 has n! isomorphic graphs 13

Interactive Proofs Lecture 16 What the all-powerful can convince - PowerPoint PPT Presentation

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