Private coins versus public coins in interactive proof systems
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
The knowledge complexity of interactive proof-systems
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
Does co-NP have short interactive proofs?
Information Processing Letters
Are there interactive protocols for CO-NP languages?
Information Processing Letters
Arthur-Merlin games: a randomized proof system, and a hierarchy of complexity class
Journal of Computer and System Sciences - 17th Annual ACM Symposium in the Theory of Computing, May 6-8, 1985
Multi-prover interactive proofs: how to remove intractability assumptions
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Complexity classes defined by counting quantifiers
Journal of the ACM (JACM)
PP is as hard as the polynomial-time hierarchy
SIAM Journal on Computing
A note on efficient zero-knowledge proofs and arguments (extended abstract)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Algebraic methods for interactive proof systems
Journal of the ACM (JACM)
Journal of the ACM (JACM)
On the power of multi-prover interactive protocols
Theoretical Computer Science
P = BPP if E requires exponential circuits: derandomizing the XOR lemma
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Making games short (extended abstract)
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
SIAM Journal on Computing
Universal Arguments and their Applications
CCC '02 Proceedings of the 17th IEEE Annual Conference on Computational Complexity
Rational secret sharing and multiparty computation: extended abstract
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Non-cooperative computation: boolean functions with correctness and exclusivity
Theoretical Computer Science - Game theory meets theoretical computer science
COMPUTATIONALLY PRIVATE RANDOMIZING POLYNOMIALS AND THEIR APPLICATIONS
Computational Complexity
Delegating computation: interactive proofs for muggles
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Proofs that yield nothing but their validity and a methodology of cryptographic protocol design
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
Probabilistically Checkable Arguments
CRYPTO '09 Proceedings of the 29th Annual International Cryptology Conference on Advances in Cryptology
Bridging game theory and cryptography: recent results and future directions
TCC'08 Proceedings of the 5th conference on Theory of cryptography
Non-interactive verifiable computing: outsourcing computation to untrusted workers
CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
Improved delegation of computation using fully homomorphic encryption
CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
Only valuable experts can be valued
Proceedings of the 12th ACM conference on Electronic commerce
Optimal verification of operations on dynamic sets
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
Practical delegation of computation using multiple servers
Proceedings of the 18th ACM conference on Computer and communications security
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Super-efficient rational proofs
Proceedings of the fourteenth ACM conference on Electronic commerce
Rational arguments: single round delegation with sublinear verification
Proceedings of the 5th conference on Innovations in theoretical computer science
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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.