lecture17

# lecture17 - WHAT IS A PROOF CSci 5403 G HAM v1,v2,vn...

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1 COMPLEXITY THEORY CSci 5403 LECTURE XVII: INTERACTIVE PROOFS I WHAT IS A PROOF ? G ˥ HAM: Quite So. A traditional proof is an efficiently verifiable static sequence of symbols that establishes that x ˥ L. Prover Verifier NP = { languages with “short” proofs } v 1 ,v 2 ,…,v n INTERACTIVE PROOFS x ˥ L: … Unbounded Prover Efficient Verifier …? …? almost certainly so. GNI = { ʪ G,H ʫ | |G|=|H| and G H } ISO ˥ NP ˰ GNI coNP. Is GNI ˥ NP? Graphs G and H are isomorphic, written G H, if ˳ bijection π : V G V H so that (u,v) ˥ E G iff ( π (u), π (v)) ˥ E H . b a e c d 2 1 5 3 4 ISO = { ʪ G,H ʫ | G H }

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2 Traditional Prover INTERACTIVE PROOFS Unbounded Prover Efficient Verifier π (G b ) b Intriguing. G 0 G 1 The proof is too long for you to read. I am crushed. INTERACTIVE PROOFS Definition. An interactive proof system has two players: Arbitrary Prover P : Σ * Σ * α 1 = V(x;r) α 2 = P(x, α 1 ) α k = P(x, α 1 , α 2 ,…, α k-1 ) α k+1 = accept/reject The conversation (V P)(x;r) is α
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• Spring '08
• Sturtivant,C
• Computational complexity theory, GNI, Interactive proof system, interactive proof, interactive proofs

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lecture17 - WHAT IS A PROOF CSci 5403 G HAM v1,v2,vn...

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