Questions tagged [interactive-proof-systems]

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“Essential” problem for MA

I am trying to understand different interactive proof systems, in particular AM and MA. Is there a typical problem for the complexity class MA as Graph-NonIsomorphism problem is for AM? Is there ...
4
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109 views

Interactive proofs for coNP languages proof clarification

I was reading a paper by Lance Fortnow and Michael Sipser. "Are there interactive protocols for co-NP languages?" Information Processing Letters 28 v5 (1988), pp. 249-251. An online version of the ...
2
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Why the soundness error in the $\mathrm{IP}$ of GNI can implicate $\mathrm{\Sigma_2} \subseteq \mathrm{\Pi_2}$ if GNI is co-NP-Complete?

PDF here shows a way to proof GI is NP-Complete $\implies \Sigma_2 = \Pi_2$. In the last step, it writes following: In other words, (1) is false in this case as required. Book Computational ...
1
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Proving (relativized) upper bounds against SZK

Does anyone know of any instances where we've been able to show that some complexity class is strictly harder than SZK relative to some oracle? In general, it seems that SZK is really hard (for ...
1
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12 views

Practical applications of multi-prover interactive proof protocols

A multi-prover interactive proof protocol, as described here, consists of computationally unbound provers $P_1,P_2,\ldots$ which together convince a polynomial-time verifier $V$ of some proposition, ...
1
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115 views

Perfect Completeness of AM protocols?

I understand the idea behind making a MA protocol perfectly complete. In a MA protocol, Merlin sends a proof $\pi$ which Arthur checks with his machine $V$ by plugging in some random bits $r$ such ...
1
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78 views

Interactive protocols for showing knots are “hard” to untie

Given two graphs $G_1$ and $G_2$, a zero-knowledge interactive protocol for a prover to convince a verifier that $G_1\not\cong G_2$ entails: The verifier choosing a random $i\in\{1,2\}$ The verifier ...
1
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0answers
62 views

Why does the proof that #SAT is in IP stop after m rounds?

I've been struggling to understand why the interactive proof for #SAT stops after only $m$ rounds, where $m$ is the number of variables in the formula $\phi$. I understand that two polynomials of ...
1
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53 views

Use of Mizar for algorithm specification and automatic analysis and discovery of algorithms?

Is it possible to use Mizar Mathematical Library for the specification of algorithms at the same detalization level as the implementation of the algorithm in industrial programming language? Mizar ...
1
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50 views

Reasoning approaches for implementing a Knowledge-based System?

What are the major approaches in implementing a Knowledge-based System (KBS)? Approaches used to take decisions in a KBS that I have come across so far are the case-based and rule-based reasoning ...
0
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1answer
76 views

How to remove a universal quantifier in Lean theorem prover

I am working with two binary relations: g_o and pw_o, and I've defined pw_o below: constants {A : Type} (g_o : A → A → Prop) ...