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We show NP-completeness for several planar variants of the monotone satisfiability problem with bounded variable appearances. With one exception the presented variants have an associated bipartite graph where the vertex degree is bounded by…
We investigate the problem of testing whether a discrete probability distribution over an ordered domain is a histogram on a specified number of bins. One of the most common tools for the succinct approximation of data, $k$-histograms over…
We improve lower bounds on the $k$th-order nonlinear complexity of pseudorandom sequences over finite fields and we establish a probabilistic result on the behavior of the $k$th-order nonlinear complexity of random sequences over finite…
We consider the problem of high-dimensional non-linear variable selection for supervised learning. Our approach is based on performing linear selection among exponentially many appropriately defined positive definite kernels that…
The purpose of this paper is to provide efficient algorithms that decide membership for classes of several Boolean hierarchies for which efficiency (or even decidability) were previously not known. We develop new forbidden-chain…
We study the sample complexity of nondeterministically testable graph parameters and improve existing bounds on it by several orders of magnitude. The technique used would be also of independent interest. We also discuss the special case of…
Deep Q-learning based algorithms have been applied successfully in many decision making problems, while their theoretical foundations are not as well understood. In this paper, we study a Fitted Q-Iteration with two-layer ReLU neural…
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…
Computational models typically assume that operations are applied in a fixed sequential order. In recent years several works have looked at relaxing this assumption, considering computations without any fixed causal structure and showing…
The performance of a neural network for a given task is largely determined by the initial calibration of the network parameters. Yet, it has been shown that the calibration, also referred to as training, is generally NP-complete. This…
We present a comprehensive review of the nodal domains and lines of quantum billiards, emphasizing a quantitative comparison of theoretical findings to experiments. The nodal statistics are shown to distinguish not only between regular and…
Relations between the decision tree complexity and various other complexity measures of Boolean functions is a thriving topic of research in computational complexity. It is known that decision tree complexity is bounded above by the cube of…
This paper presents a complete algorithmic study of the decision Boolean Satisfiability Problem under the classical computation and quantum computation theories. The paper depicts deterministic and probabilistic algorithms, propositions of…
It is known that quantum computers yield a speed-up for certain discrete problems. Here we want to know whether quantum computers are useful for continuous problems. We study the computation of the integral of functions from the classical…
Quantum span program algorithms for function evaluation commonly have reduced query complexity when promised that the input has a certain structure. We design a modified span program algorithm to show these speed-ups persist even without…
Suppose we have n algorithms, quantum or classical, each computing some bit-value with bounded error probability. We describe a quantum algorithm that uses O(sqrt{n}) repetitions of the base algorithms and with high probability finds the…
Many planning formalisms allow for mixing numeric with Boolean effects. However, most of these formalisms are undecidable. In this paper, we will analyze possible causes for this undecidability by studying the number of different…
K-fold cross-validation is a widely used tool for assessing classifier performance. The reproducibility crisis faced by artificial intelligence partly results from the irreproducibility of reported k-fold cross-validation-based performance…
Decision Diagrams(DDs) are one of the most popular representations for boolean functions. They are widely used in the design and verification of circuits. Different types of DDs have been proven to represent important functions in…
Decision diagrams (DDs) have emerged as an efficient tool for simulating quantum circuits due to their capacity to exploit data redundancies in quantum states and quantum operations, enabling the efficient computation of probability…