Related papers: Direct sum theorems beyond query complexity
Query complexity is a common tool for comparing quantum and classical computation, and it has produced many examples of how quantum algorithms differ from classical ones. Here we investigate in detail the role that oracles play for the…
The discovery of derivatives and integrals was a tremendous leap in scientific knowledge and completely revolutionized many fields, including mathematics, physics, and engineering. The existence of higher-order derivatives means better…
This paper establishes theoretical bonafides for implicit concurrent multivariate effect evaluation--implicit concurrency for short---a broad and versatile computational learning efficiency thought to underlie general-purpose, non-local,…
Grover's algorithm is a primary algorithm offered as evidence that quantum computers can provide an advantage over classical computers. It involves an "oracle" specified for a given application whose structure is not part of the formal…
This paper studies the lower bound complexity for the optimization problem whose objective function is the average of $n$ individual smooth convex functions. We consider the algorithm which gets access to gradient and proximal oracle for…
Complex reasoning problems are most clearly and easily specified using logical rules, but require recursive rules with aggregation such as count and sum for practical applications. Unfortunately, the meaning of such rules has been a…
There exists a well established differential topological theory of singularities of ordinary differential equations. It has mainly studied scalar equations of low order. We propose an extension of the key concepts to arbitrary systems of…
We study classical query algorithms with post-selection, and find that they are closely connected to rational functions with nonnegative coefficients. We show that the post-selected classical query complexity of a Boolean function is equal…
Quantum computing has advanced rapidly in recent years and has shown advantages in a variety of domains. In this paper, we investigate its potential for discrete simulation optimization in the fixed-confidence setting, a fundamental problem…
The 3SUM problem is one of the cornerstones of fine-grained complexity. Its study has led to countless lower bounds, but as has been sporadically observed before -- and as we will demonstrate again -- insights on 3SUM can also lead to…
A rational function $f(x)$ is rationally summable if there exists a rational function $g(x)$ such that $f(x)=g(x+1)-g(x)$. Detecting whether a given rational function is summable is an important and basic computational subproblem that…
Quantum theory is consistent with a computational model permitting black-box operations to be applied in an indefinite causal order, going beyond the standard circuit model of computation. The quantum switch -- the simplest such example --…
Several well-studied models of access to data samples, including statistical queries, local differential privacy and low-communication algorithms rely on queries that provide information about a function of a single sample. (For example, a…
Equality and disjointness are two of the most studied problems in communication complexity. They have been studied for both classical and also quantum communication and for various models and modes of communication. Buhrman et al. [Buh98]…
In this paper, we consider smooth convex optimization problems with simple constraints and inexactness in the oracle information such as value, partial or directional derivatives of the objective function. We introduce a unifying framework,…
This paper develops a new framework for indirect statistical inference with guaranteed necessity and sufficiency, applicable to continuous random variables. We prove that when comparing exponentially transformed order statistics from an…
A proof of quantumness is an efficiently verifiable interactive test that an efficient quantum computer can pass, but all efficient classical computers cannot (under some cryptographic assumption). Such protocols play a crucial role in the…
When a computer algebra system fails to solve an Ordinary Differential Equation, is this a limitation of its implementation, or a genuine computational barrier? Three traditions bear on the question. Modern computer algebra algorithms can…
Three decades of research in communication complexity have led to the invention of a number of techniques to lower bound randomized communication complexity. The majority of these techniques involve properties of large submatrices…
We study an interval ordering problem introduced by D\"urr et al. [Discrete Appl. Math. 2012] which is motivated by applications in bioinformatics. The task is to order a given set of n intervals with the goal of minimizing a certain…