Related papers: Certificate complexity and symmetry of nested cana…
This is the second in a series of articles aimed at exploring the relationship between the complexity classes of P and NP. The research in this article aims to find conditions of an algorithmic nature that are necessary and sufficient to…
Verifying robustness of neural network classifiers has attracted great interests and attention due to the success of deep neural networks and their unexpected vulnerability to adversarial perturbations. Although finding minimum adversarial…
Nested dichotomies are used as a method of transforming a multiclass classification problem into a series of binary problems. A tree structure is induced that recursively splits the set of classes into subsets, and a binary classification…
Various key problems from theoretical computer science can be expressed as polynomial optimization problems over the boolean hypercube. One particularly successful way to prove complexity bounds for these types of problems are based on sums…
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 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,…
Safety is a fundamental requirement of control systems. Control Barrier Functions (CBFs) are proposed to ensure the safety of the control system by constructing safety filters or synthesizing control inputs. However, the safety guarantee…
Barrier certificates, a form of state invariants, provide an automated approach to the verification of the safety of dynamical systems. Similarly to barrier certificates, recent works explore the notion of closure certificates, a form of…
Normalizing Flows (NFs) are able to model complicated distributions p(y) with strong inter-dimensional correlations and high multimodality by transforming a simple base density p(z) through an invertible neural network under the change of…
In this paper we study the complexity of quantum query algorithms computing the value of Boolean function and its relation to the degree of algebraic polynomial representing this function. We pay special attention to Boolean functions with…
Secure multi-party computation using a physical deck of cards, often called card-based cryptography, has been extensively studied during the past decade. Card-based protocols to compute various Boolean functions have been developed. As each…
We investigate the computational complexity of neural network verification in quantised settings. We distinguish three classes of Feedforward Neural Networks (FNNs): rational FNNs with exact rational weights, quantised FNNs whose weights…
In this paper we consider the safety verification and safe controller synthesis problems for nonlinear control systems. The Control Barrier Certificates (CBC) approach is proposed as an extension to the Barrier certificates approach. Our…
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…
Given a small random sample of $n$-bit strings labeled by an unknown Boolean function, which properties of this function can be tested computationally efficiently? We show an equivalence between properties that are efficiently testable from…
We show that for any constant $c>0$, any (two-sided error) adaptive algorithm for testing monotonicity of Boolean functions must have query complexity $\Omega(n^{1/2-c})$. This improves the $\tilde\Omega(n^{1/3})$ lower bound of [CWX17] and…
In this paper, we study the graph realization problem in the Congested Clique model of distributed computing under crash faults. We consider {\em degree-sequence realization}, in which each node $v$ is associated with a degree value $d(v)$,…
In this paper, we consider the problem of certifying the robustness of neural networks to perturbed and adversarial input data. Such certification is imperative for the application of neural networks in safety-critical decision-making and…
Function-level binary code similarity detection is a crucial aspect of cybersecurity. It enables the detection of bugs and patent infringements in released software and plays a pivotal role in preventing supply chain attacks. A practical…
Here we consider an approach for fast computing the algebraic degree of Boolean functions. It combines fast computing the ANF (known as ANF transform) and thereafter the algebraic degree by using the weight-lexicographic order (WLO) of the…