Related papers: Decision Tree Complexity versus Block Sensitivity …
We investigate the computation of minimum-cost spanning trees satisfying prescribed vertex degree constraints: Given a graph $G$ and a constraint function $D$, we ask for a (minimum-cost) spanning tree $T$ such that for each vertex $v$, $T$…
In this note we compare two measures of the complexity of a class $\mathcal F$ of Boolean functions studied in (unconditional) pseudorandomness: $\mathcal F$'s ability to distinguish between biased and uniform coins (the coin problem), and…
Decision trees partition the feature space using hard binary thresholds, assigning identical confidence to instances far from a decision boundary and to those directly on it. We introduce ternary decision trees, which augment each split…
The Sensitivity Conjecture is a long-standing problem in theoretical computer science that seeks to fit the sensitivity of a Boolean function into a unified framework formed by the other complexity measures of Boolean functions, such as…
Systems of decision rules and decision trees are widely used as a means for knowledge representation, as classifiers, and as algorithms. They are among the most interpretable models for classifying and representing knowledge. The study of…
We consider the problem of testing whether a Boolean function has Fourier degree $\leq k$ or it is $\epsilon$-far from any Boolean function with Fourier degree $\leq k$. We improve the known lower bound of $\Omega(k)$ \cite{BBM11,CGM10}, to…
This paper discovers that the neural network with lower decision boundary (DB) variability has better generalizability. Two new notions, algorithm DB variability and $(\epsilon, \eta)$-data DB variability, are proposed to measure the…
We introduce a theoretical framework for understanding and predicting the complexity of sequence classification tasks, using a novel extension of the theory of Boolean function sensitivity. The sensitivity of a function, given a…
Polynomial threshold functions (PTFs) are an important low-complexity class of Boolean functions, with strong connections to learning theory and approximation theory. Recent work on learning and testing PTFs has exploited structural and…
We define a measure for the complexity of Boolean functions related to their implementation in neural networks, and in particular close related to the generalization ability that could be obtained through the learning process. The measure…
Can deep learning solve multiple tasks simultaneously, even when they are unrelated and very different? We investigate how the representations of the underlying tasks affect the ability of a single neural network to learn them jointly. We…
The tree-width of a multivariate polynomial is the tree-width of the hypergraph with hyperedges corresponding to its terms. Multivariate polynomials of bounded tree-width have been studied by Makowsky and Meer as a new sparsity condition…
In this paper, we consider classes of decision tables with many-valued decisions closed under operations of removal of columns, changing of decisions, permutation of columns, and duplication of columns. We study relationships among three…
Balliu et al. (DISC 2020) classified the hardness of solving binary labeling problems with distributed graph algorithms; in these problems the task is to select a subset of edges in a $2$-colored tree in which white nodes of degree $d$ and…
Let $f:\{0,1\}^n \rightarrow \{0,1\}$ be a Boolean function. The certificate complexity $C(f)$ is a complexity measure that is quadratically tight for the zero-error randomized query complexity $R_0(f)$: $C(f) \leq R_0(f) \leq C(f)^2$. In…
In the recent years, branch-and-cut algorithms have been the target of data-driven approaches designed to enhance the decision making in different phases of the algorithm such as branching, or the choice of cutting planes (cuts). In…
A major open problem in communication complexity is whether or not quantum protocols can be exponentially more efficient than classical protocols on _total_ Boolean functions in the two-party interactive model. The answer appears to be…
We address the problem of finding optimal strategies for computing Boolean symmetric functions. We consider a collocated network, where each node's transmissions can be heard by every other node. Each node has a Boolean measurement and we…
The field of knowledge compilation establishes the tractability of many tasks by studying how to compile them to Boolean circuit classes obeying some requirements such as structuredness, decomposability, and determinism. However, in other…
In this paper we study the separation between the deterministic (classical) query complexity ($D$) and the exact quantum query complexity ($Q_E$) of several Boolean function classes using the parity decision tree method. We first define the…