Related papers: Sensitivity and Query Complexity under Uncertainty
We give an adaptive algorithm which tests whether an unknown Boolean function $f\colon \{0, 1\}^n \to\{0, 1\}$ is unate, i.e. every variable of $f$ is either non-decreasing or non-increasing, or $\epsilon$-far from unate with one-sided…
We study nondeterministic quantum algorithms for Boolean functions f. Such algorithms have positive acceptance probability on input x iff f(x)=1. In the setting of query complexity, we show that the nondeterministic quantum complexity of a…
Boolean matching is significant to digital integrated circuits design. An exhaustive method for Boolean matching is computationally expensive even for functions with only a few variables, because the time complexity of such an algorithm for…
The main reason for query model's prominence in complexity theory and quantum computing is the presence of concrete lower bounding techniques: polynomial and adversary method. There have been considerable efforts to give lower bounds using…
We consider a probability distribution on the set of Boolean functions in n variables which is induced by random Boolean expressions. Such an expression is a random rooted plane tree where the internal vertices are labelled with connectives…
The goal of the paper is to relate complexity measures associated with the evaluation of Boolean functions (certificate complexity, decision tree complexity) and learning dimensions used to characterize exact learning (teaching dimension,…
In this article we give several new results on the complexity of algorithms that learn Boolean functions from quantum queries and quantum examples. Hunziker et al. conjectured that for any class C of Boolean functions, the number of quantum…
Using Machine Learning systems in the real world can often be problematic, with inexplicable black-box models, the assumed certainty of imperfect measurements, or providing a single classification instead of a probability distribution. This…
Researchers have proposed several approaches for neural network (NN) based uncertainty quantification (UQ). However, most of the approaches are developed considering strong assumptions. Uncertainty quantification algorithms often perform…
A number of complexity measures for Boolean functions have previously been introduced. These include (1) sensitivity, (2) block sensitivity, (3) witness complexity, (4) subcube partition complexity and (5) algorithmic complexity. Each of…
We generalize and extend the ideas in a recent paper of Chiarelli, Hatami and Saks to prove new bounds on the number of relevant variables for boolean functions in terms of a variety of complexity measures. Our approach unifies and refines…
We study how to utilize (possibly erroneous) predictions in a model for computing under uncertainty in which an algorithm can query unknown data. Our aim is to minimize the number of queries needed to solve the minimum spanning tree…
We present new algorithms to compute fundamental properties of a Boolean function given in truth-table form. Specifically, we give an O(N^2.322 log N) algorithm for block sensitivity, an O(N^1.585 log N) algorithm for `tree decomposition,'…
The problem of constructing hazard-free Boolean circuits dates back to the 1940s and is an important problem in circuit design. Our main lower-bound result unconditionally shows the existence of functions whose circuit complexity is…
In this tutorial, we will survey known results on the complexity of conjunctive query evaluation in different settings, ranging from Boolean queries over counting to more complex models like enumeration and direct access. A particular focus…
This article is motivated by the following satisfiability question: pick uniformly at random an and/or Boolean expression of length n, built on a set of k_n Boolean variables. What is the probability that this expression is satisfiable?…
We study how to utilize (possibly machine-learned) predictions in a model for computing under uncertainty in which an algorithm can query unknown data. The goal is to minimize the number of queries needed to solve the problem. We consider…
This paper investigates the learnability of the nonlinearity property of Boolean functions using neural networks. We train encoder style deep neural networks to learn to predict the nonlinearity of Boolean functions from examples of…
An uncertain database is defined as a relational database in which primary keys need not be satisfied. A repair (or possible world) of such database is obtained by selecting a maximal number of tuples without ever selecting two distinct…
We investigate at decision trees that incorporate both traditional queries based on one attribute and queries based on hypotheses about the values of all attributes. Such decision trees are similar to ones studied in exact learning, where…