相关论文: Comparing Computational Power

Transformers are being used extensively across several sequence modeling tasks. Significant research effort has been devoted to experimentally probe the inner workings of Transformers. However, our conceptual and theoretical understanding…

As simulations of quantum systems cross the limits of classical computability, both quantum and classical approaches become hard to verify. Scaling predictions are therefore based on local structure and asymptotic assumptions, typically…

Reverse mathematics studies which subsystems of second order arithmetic are equivalent to key theorems of ordinary, non-set-theoretic mathematics. The main philosophical application of reverse mathematics proposed thus far is foundational…

Quantum computation is a promising emerging technology which, compared to conventional computation, allows for substantial speed-ups e.g. for integer factorization or database search. However, since physical realizations of quantum…

The nature of quantum computation is discussed. It is argued that, in terms of the amount of information manipulated in a given time, quantum and classical computation are equally efficient. Quantum superposition does not permit quantum…

Church's thesis claims that all effecticely calculable functions are recursive. A shortcoming of the various definitions of recursive functions lies in the fact that it is not a matter of a syntactical check to find out if an entity gives…

We investigate the computational properties of basic mathematical notions pertaining to $\mathbb{R}\rightarrow \mathbb{R}$-functions and subsets of $\mathbb{R}$, like finiteness, countability, (absolute) continuity, bounded variation,…

With the increasing deployment of machine learning systems in practice, transparency and explainability have become serious issues. Contrastive explanations are considered to be useful and intuitive, in particular when it comes to…

We investigate the dividing line between classical and quantum computational power in estimating properties of matrix functions. More precisely, we study the computational complexity of two primitive problems: given a function $f$ and a…

For any class of operators which transform unary total functions in the set of natural numbers into functions of the same kind, we define what it means for a real function to be uniformly computable or conditionally computable with respect…

We briefly review what a quantum computer is, what it promises to do for us, and why it is so hard to build one. Among the first applications anticipated to bear fruit is quantum simulation of quantum systems. While most quantum computation…

Transcendental functions, such as exponentials and logarithms, appear in a broad array of computational domains: from simulations in curvilinear coordinates, to interpolation, to machine learning. Unfortunately they are typically expensive…

Calculi with control operators have been studied to reason about control in programming languages and to interpret the computational content of classical proofs. To make these calculi into a real programming language, one should also…

Over the last decades, deep neural networks based-models became the dominant paradigm in machine learning. Further, the use of artificial neural networks in symbolic learning has been seen as increasingly relevant recently. To study the…

The extensive deployment of probabilistic algorithms has radically changed our perspective on several well-established computational notions. Correctness is probably the most basic one. While a typical probabilistic program cannot be said…

It is shown that a quantum computer can test the convexity and monotonicity of a given function exponentially more efficiently than a classical computer. This establishes another prominent example that showcases the potential of quantum…

There is a growing consensus that physics majors need to learn computational skills, but many departments are still devoid of computation in their physics curriculum. Some departments may lack the resources or commitment to create a…

Contrary to the classical case, the relation between quantum programming languages and quantum Turing Machines (QTM) has not being fully investigated. In particular, there are features of QTMs that have not been exploited, a notable example…

Recent research has demonstrated that quantum computers can solve certain types of problems substantially faster than the known classical algorithms. These problems include factoring integers and certain physics simulations. Practical…

Turing computability is the standard computability paradigm which captures the computational power of digital computers. To understand whether one can create physically realistic devices which have super-Turing power, one needs to…