Rational proofs
Name
Azar, Micali (2012) Rational proofs.pdf
Description
Final published version.
Size
2.18 MB
Format
Adobe PDF
Checksum (MD5)
9c759878485af40afececeb1d747307c
Author(s)
Azar, Pablo Daniel
Micali, Silvio
Date Issued
May 19, 2012
Publisher
© Association for Computing Machinery, New York, NY, USA
Citation
Azar, P. D., & Micali, S. (2012). Rational proofs. Proceedings of the Forty-Fourth Annual ACM Symposium on Theory of Computing (STOC '12), 1017–1028.
Version
Final published version.
Abstract
We study a new type of proof system, where an unbounded prover and a polynomial time verifier interact, on inputs a string x and a function f , so that the Verifier may learn f (x). The novelty of our setting is that there no longer are “good” or “malicious” provers, but only rational ones. In essence, the Verifier has a budget c and gives the Prover a reward r ∈ [0, c] determined by the transcript of their interaction; the prover wishes to maximize his expected reward; and his reward is maximized only if he the verifier correctly learns f (x).
Rational proof systems are as powerful as their classical counterparts for polynomially many rounds of interaction, but are much more powerful when we only allow a constant number of rounds. Indeed, we prove that if f ∈ #P, then f is computable by a one-round rational Merlin-Arthur game, where, on input x, Merlin’s single message actually consists of sending just the value f(x). Further, we prove that CH, the counting hierarchy, coincides with the class of languages computable by a constant-round rational Merlin- Arthur game.
Our results rely on a basic and crucial connection between rational proof systems and proper scoring rules, a tool developed to elicit truthful information from experts.
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