Related papers: Bad oracles in higher computability and randomness
Algorithms with unitary oracles can be nested, which makes them extremely versatile. An example is the phase estimation algorithm used in many candidate algorithms for quantum speed-up. The search for new quantum algorithms benefits from…
Most machine learning classifiers, including deep neural networks, are vulnerable to adversarial examples. Such inputs are typically generated by adding small but purposeful modifications that lead to incorrect outputs while imperceptible…
Pairwise "same-cluster" queries are one of the most widely used forms of supervision in semi-supervised clustering. However, it is impractical to ask human oracles to answer every query correctly. In this paper, we study the influence of…
Different types of reasoning impose different structural demands on representational systems, yet no systematic account of these demands exists across psychology, AI, and philosophy of mind. I propose a framework identifying four structural…
Combinatorics, like computer science, often has to deal with large objects of unspecified (or unusable) structure. One powerful way to deal with such an arbitrary object is to decompose it into more usable components. In particular, it has…
A set is autoreducible if it can be reduced to itself by a Turing machine that does not ask its own input to the oracle. We use autoreducibility to separate the polynomial-time hierarchy from polynomial space by showing that all…
We consider various collections of functions from the Baire space X into itself naturally arising in (effective) descriptive set theory and general topology, including computable (equivalently, recursive) functions, contraction mappings,…
Higher-order quantum theory deals with causal quantum processes, described by quantum combs, and test procedures, described by quantum testers, "measuring" these processes. In this work, we show that "jointly non-implementable" or…
To reduce the danger of powerful super-intelligent AIs, we might make the first such AIs oracles that can only send and receive messages. This paper proposes a possibly practical means of using machine learning to create two classes of…
In this paper we provide a broad framework for describing learning agents in general quantum environments. We analyze the types of classically specified environments which allow for quantum enhancements in learning, by contrasting…
We use the powerful tools of counting complexity and generic oracles to help understand the limitations of the complexity of quantum computation. We show several results for the probabilistic quantum class BQP. 1. BQP is low for PP, i.e.,…
In previous work, we have combined computable structure theory and algorithmic learning theory to study which families of algebraic structures are learnable in the limit (up to isomorphism). In this paper, we measure the computational power…
We provide the first evidence for the inherent difficulty of finding complex sets with optimal proof systems. For this, we construct oracles $O_1$ and $O_2$ with the following properties, where $\mathrm{RE}$ denotes the class of recursively…
In this article, we will show that uncomputability is a relative property not only of oracle Turing machines, but also of subrecursive classes. We will define the concept of a Turing submachine, and a recursive relative version for the Busy…
We construct a quantum oracle relative to which $\mathsf{BQP} = \mathsf{QMA}$ but cryptographic pseudorandom quantum states and pseudorandom unitary transformations exist, a counterintuitive result in light of the fact that pseudorandom…
We propose cloud oracles, an alternative to machine learning for online optimization of cloud configurations. Our cloud oracle approach guarantees complete accuracy and explainability of decisions for problems that can be formulated as…
In combinatorics, the probabilistic method is a very powerful tool to prove the existence of combinatorial objects with interesting and useful properties. Explicit constructions of objects with such properties are often very difficult, or…
This article expands our work in [Ca16]. By its reliance on Turing computability, the classical theory of effectivity, along with effective reducibility and Weihrauch reducibility, is only applicable to objects that are either countable or…
It is possible that powerful and potentially dangerous artificial intelligence (AI) might be developed in the future. An Oracle is a design which aims to restrain the impact of a potentially dangerous AI by restricting the agent to no…
One can fix the randomness used by a randomized algorithm, but there is no analogous notion of fixing the quantumness used by a quantum algorithm. Underscoring this fundamental difference, we show that, in the black-box setting, the…