Related papers: On K-wise Independent Distributions and Boolean Fu…
We introduce a simply stated conjecture regarding the maximum mutual information a Boolean function can reveal about noisy inputs. Specifically, let $X^n$ be i.i.d. Bernoulli(1/2), and let $Y^n$ be the result of passing $X^n$ through a…
We present an $\tilde{O}(n^{2/3}/\epsilon^2)$-query algorithm that tests whether an unknown Boolean function $f\colon\{0,1\}^n\rightarrow \{0,1\}$ is unate (i.e., every variable is either non-decreasing or non-increasing) or $\epsilon$-far…
Typical properties of computing circuits composed of noisy logical gates are studied using the statistical physics methodology. A growth model that gives rise to typical random Boolean functions is mapped onto a layered Ising spin system,…
We study the quantum query complexity of the Boolean hidden shift problem. Given oracle access to f(x+s) for a known Boolean function f, the task is to determine the n-bit string s. The quantum query complexity of this problem depends…
Local consistency arises in diverse areas, including Bayesian statistics, relational databases, and quantum foundations, and so does the notion of functional dependence. We adopt a general approach to study logical inference in a setting…
Motivated by the recent work on asymptotic independence relations for random matrices with non-commutative entries, we investigate the limit distribution and independence relations for large matrices with identically distributed and Boolean…
We study the extremal competitive ratio of Boolean function evaluation. We provide the first non-trivial lower and upper bounds for classes of Boolean functions which are not included in the class of monotone Boolean functions. For the…
A function f : {0, 1}^n -> {0, 1} is said to be k-monotone if it flips between 0 and 1 at most k times on every ascending chain. Such functions represent a natural generalization of (1-)monotone functions, and have been recently studied in…
The model of relative-error property testing of Boolean functions has been the subject of significant recent research effort [CDH+24][CPPS25a][CPPS25b] In this paper we consider the problem of relative-error testing an unknown and arbitrary…
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 consider the Stochastic Boolean Function Evaluation (SBFE) problem where the task is to efficiently evaluate a known Boolean function $f$ on an unknown bit string $x$ of length $n$. We determine $f(x)$ by sequentially testing the…
This paper reviews a class of generic dissipative dynamical systems called N-K models. In these models, the dynamics of N elements, defined as Boolean variables, develop step by step, clocked by a discrete time variable. Each of the N…
Bent Boolean functions are important objects in cryptography and coding theory, and there are several general approaches for constructing such functions. Metaheuristics proved to be a strong choice as they can provide many bent functions,…
We prove the "Most informative boolean function" conjecture of Courtade and Kumar for high noise $\epsilon \ge 1/2 - \delta$, for some absolute constant $\delta > 0$. Namely, if $X$ is uniformly distributed in $\{0,1\}^n$ and $Y$ is…
This paper studies the mathematical properties of collectively canalizing Boolean functions, a class of functions that has arisen from applications in systems biology. Boolean networks are an increasingly popular modeling framework for…
A Boolean function $f:\{0,1\}^n\to \{0,1\}$ is $k$-linear if it returns the sum (over the binary field $F_2$) of $k$ coordinates of the input. In this paper, we study property testing of the classes $k$-Linear, the class of all $k$-linear…
Suppose that $Y^n$ is obtained by observing a uniform Bernoulli random vector $X^n$ through a binary symmetric channel with crossover probability $\alpha$. The "most informative Boolean function" conjecture postulates that the maximal…
For three decades binary decision diagrams, a data structure efficiently representing Boolean functions, have been widely used in many distinct contexts like model verification, machine learning, cryptography and also resolution of…
Boolean functions with strong cryptographic properties, such as high nonlinearity and algebraic degree, are important for the security of stream and block ciphers. These functions can be designed using algebraic constructions or…
Boolean functions are mathematical objects used in diverse applications. Different applications also have different requirements, making the research on Boolean functions very active. In the last 30 years, evolutionary algorithms have been…