Identifying an Honest EXP^NP Oracle Among Many
نویسنده
چکیده
We provide a general framework to remove short advice by formulating the following computational task for a function f : given two oracles at least one of which is honest (i.e. correctly computes f on all inputs) as well as an input, the task is to compute f on the input with the help of the oracles by a probabilistic polynomial-time machine, which we shall call a selector. We characterize the languages for which short advice can be removed by the notion of selector: a paddable language has a selector if and only if short advice of a probabilistic machine that accepts the language can be removed under any relativized world. Previously, instance checkers have served as a useful tool to remove short advice of probabilistic computation. We indicate that existence of instance checkers is a property stronger than that of removing short advice: although no instance checker for EXPNP-complete languages exists unless EXPNP = NEXP, we prove that there exists a selector for any EXPNP-complete language, by building on the proof of MIP = NEXP by Babai, Fortnow, and Lund (1991). 1998 ACM Subject Classification F.1.1 Models of Computation;, F.1.2 Modes of Computation, F.1.3 Complexity Measures and Classes
منابع مشابه
Identifying an Honest ${\rm EXP}^{\rm NP}$ Oracle Among Many
We provide a general framework to remove short advice by formulating the following computational task for a function f : given two oracles at least one of which is honest (i.e. correctly computes f on all inputs) as well as an input, the task is to compute f on the input with the help of the oracles by a probabilistic polynomial-time machine, which we shall call a selector. We characterize the ...
متن کاملPolynomial-Time Random Oracles and Separating Complexity Classes
Bennett and Gill (1981) showed that P 6= NP 6= coNP for a random oracle A, with probability 1. We investigate whether this result extends to individual polynomial-time random oracles. We consider two notions of random oracles: p-random oracles in the sense of martingales and resource-bounded measure (Lutz, 1992; Ambos-Spies et al., 1997), and p-betting-game random oracles using the betting game...
متن کاملLimits of Minimum Circuit Size Problem as Oracle
The Minimum Circuit Size Problem (MCSP) is known to be hard for statistical zero knowledge via a BPP-reduction (Allender and Das, 2014), whereas establishing NP-hardness of MCSP via a polynomial-time many-one reduction is difficult (Murray and Williams, 2015) in the sense that it implies ZPP 6= EXP, which is a major open problem in computational complexity. In this paper, we provide strong evid...
متن کاملOn the Sparse Set Conjecture for Sets with Low Denisty
We study the sparse set conjecture for sets with low density. The sparse set conjecture states that P = NP if and only if there exists a sparse Turing hard set for NP. In this paper we study a weaker variant of the conjecture. We are interested in the consequences of NP having Tur-ing hard sets of density f (n), for (unbounded) functions f (n), that are sub-polynomial, for example log(n). We es...
متن کاملQuantum Bounded Query Complexity
We combine the classical notions and techniques for bounded query classes with those developed in quantum computing. We give strong evidence that quantum queries to an oracle in the class NP does indeed reduce the query complexity of decision problems. Under traditional complexity assumptions, we obtain an exponential speedup between the quantum and the classical query complexity of function cl...
متن کامل