A Protocol for Generating Random Elements with Their Probabilities
نویسندگان
چکیده
We give an AM protocol that allows the verifier to sample elements x from a probability distribution P, which is held by the prover. If the prover is honest, the verifier outputs (x,P(x)) with probability close to P(x). In case the prover is dishonest, one may hope for the following guarantee: if the verifier outputs (x, p), then the probability that the verifier outputs x is close to p. Simple examples show that this cannot be achieved. Instead, we show that the following weaker condition holds (in a well defined sense) on average: If (x, p) is output, then p is an upper bound on the probability that x is output. Our protocol yields a new transformation to turn interactive proofs where the verifier uses private random coins into proofs with public coins. The verifier has better running time compared to the well-known Goldwasser-Sipser transformation (STOC, 1986). For constant-round protocols, we only lose an arbitrarily small constant in soundness and completeness, while our public-coin verifier calls the private-coin verifier only once. ETH Zurich, Department of Computer Science, 8092 Zurich, Switzerland. E-mail: [email protected] ETH Zurich, Department of Computer Science, 8092 Zurich, Switzerland. E-mail: [email protected]
منابع مشابه
Probability Generating Functions for Sattolo’s Algorithm
In 1986 S. Sattolo introduced a simple algorithm for uniform random generation of cyclic permutations on a fixed number of symbols. Recently, H. Prodinger analysed two important random variables associated with the algorithm, and found their mean and variance. H. Mahmoud extended Prodinger’s analysis by finding limit laws for the same two random variables.The present article, starting from the ...
متن کاملAnalytic Samplers and the Combinatorial Rejection Method
Boltzmann samplers, introduced by Duchon et al. in 2001, make it possible to uniformly draw approximate size objects from any class which can be specified through the symbolic method. This, through by evaluating the associated generating functions to obtain the correct branching probabilities. But these samplers require generating functions, in particular in the neighborhood of their sunglarity...
متن کاملRelationships between Τ-function and Fredholm Determinant Expressions for Gap Probabilities in Random Matrix Theory
The gap probabilities at the hard and soft edges of scaled random matrix ensembles with orthogonal symmetry are known in terms of τ -functions. Extending recent work relating to the soft edge, it is shown that these τ -functions, and their generalizations to contain a generating function like parameter, can be expressed as Fredholm determinants. These same Fredholm determinants also occur in ex...
متن کاملTransient Solution of an M/M/1 Variant Working Vacation Queue with Balking
This paper presents the transient solution of a variant working vacation queue with balking. Customers arrive according to a Poisson process and decide to join the queue with probability $b$ or balk with $bar{b} = 1-b$. As soon as the system becomes empty, the server takes working vacation. The service times during regular busy period and working vacation period, and vacation times are assumed ...
متن کامل