It is well known that the optimal convergence rate for stochastic optimization of smooth functions is O(1/ √ T ), which is same as stochastic optimization of Lipschitz continuous convex functions. This is in contrast to optimizing smooth functions using full gradients, which yields a convergence rate of O(1/T ). In this work, we consider a new setup for optimizing smooth functions, termed asMix...

Most real-time scheduling problems are known to be NP-complete. To enable accurate comparison between the schedules of heuristic algorithms and the optimal schedule, we introduce an omniscient oracle. This oracle provides schedules for periodic task sets with harmonic periods and variable resource requirements. Three di erent job value functions are described and implemented. Each corresponds t...

Consider a quantum computer in combination with a binary oracle of domain size N . It is shown how N/2 + √ N calls to the oracle are sufficient to guess the whole content of the oracle (being an N bit string) with probability greater than 85%. This contrasts the power of classical computers which would require N calls to achieve the same result. From this result it follows that any binary funct...

We describe a general way of building oracle Turing machines, thereby treating oracle queries as reductions. The model allows various types of reductions, which lead to the diierent oracle models known from the literature. For model theoretic purposes we deene a functional transducer model which, for many complexity classes, corresponds to logical interpretations. We thus get a notion of reduct...

It is an established fact that for many of the interesting problems quantum algorithms based on queries of the standard oracle bring no significant improvement in comparison to known classical algorithms. It is conceivable that there are other oracles of algorithmic importance acting in a less intuitive fashion to which such limitations do not apply. Thus motivated this article suggests a broad...

The factor oracle is a relatively new data structure for the set of factors of a string. It has been introduced by Allauzen, Crochemore, and Raffinot in 1999. It may recognize nonfactors (hence the name “oracle”) but its implementational simplicity and experimental behaviour are stunning; factor oracle based string matching has been conjectured optimal on average. However, its structure is not ...

Ensemble methods with Random Oracles have been proposed recently (Kuncheva and Rodŕıguez, 2007). A random-oracle classifier consists of a pair of classifiers and a fixed, randomly created oracle that selects between them. Ensembles of random-oracle decision trees were shown to fare better than standard ensembles. In that study, the oracle for a given tree was a random hyperplane at the root of ...

An Oracle is a design for potentially high power artificial intelligences (AIs), where the AI is made safe by restricting it to only answer questions. Unfortunately most designs cause the Oracle to be motivated to manipulate humans with the contents of their answers, and Oracles of potentially high intelligence might be very successful at this. Solving the problem, without compromising the accu...

7 We consider polynomial-time Turing machines that have access to two oracles and investigate when the order of oracle queries is significant. The oracles used here are complete languages for the Polynomial Hierarchy (PH). We prove that, for solving decision problems, the order of oracle queries does not matter. This improves upon the previous result of Hemaspaandra, Hemaspaandra and Hempel, wh...

For relativized arguments, we propose to restrict oracle queries to “stringent” ones. For example, when comparing the power of two machine models relative to some oracle set X, we restrict that machines of both types ask queries from the same segment of the set X. In particular, for investigating polynomial-time (or polynomial-size) computability, we propose polynomial stringency, bounding quer...