Rational proofs
Name
Micali_Rational Proofs.pdf
Size
329.69 KB
Format
Adobe PDF
Checksum (MD5)
8f14085a825295e3a4c1180fc27b48af
Author(s)
Azar, Pablo Daniel
Micali, Silvio
Date Issued
May 2012
Journal
Proceedings of the 44th symposium on Theory of Computing (STOC '12 )
Publisher
Association for Computing Machinery (ACM)
Citation
Azar, Pablo Daniel, and Silvio Micali. “Rational Proofs.” Proceedings of the 44th symposium on Theory of Computing (STOC '12 ). 1017.
Version
Author's final manuscript
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.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike 3.0
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1145/2213977.2214069
