Related papers: Exploring Semi-bent Boolean Functions Arising from…
We propose a general approach to construct cryptographic significant Boolean functions of $(r+1)m$ variables based on the additive decomposition $\mathbb{F}_{2^{rm}}\times\mathbb{F}_{2^m}$ of the finite field $\mathbb{F}_{2^{(r+1)m}}$,…
Boolean functions with high algebraic immunity are important cryptographic primitives in some stream ciphers. In this paper, two methodologies for constructing binary minimal codes from sets, Boolean functions and vectorial Boolean…
Number-conserving (or {\em conservative}) cellular automata have been used in several contexts, in particular traffic models, where it is natural to think about them as systems of interacting particles. In this article we consider several…
Cellular automata are capable of developing complex behaviors based on simple local interactions between their elements. Some of these characteristics have been used to propose and improve meta-heuristics for global optimization; however,…
We consider the multiplicative complexity of Boolean functions with multiple bits of output, studying how large a multiplicative complexity is necessary and sufficient to provide a desired nonlinearity. For so-called $\Sigma\Pi\Sigma$…
This paper concerns $d$-dimensional cellular automata with the von Neumann neighborhood that conserve the sum of the states of all their cells. These automata, called number-conserving or density-conserving cellular automata, are of…
This paper studies two kinds of simulation between cellular automata: simulations based on factor and simulations based on sub-automaton. We show that these two kinds of simulation behave in two opposite ways with respect to the complexity…
Computational models of biological processes provide one of the most powerful methods for a detailed analysis of the mechanisms that drive the behavior of complex systems. Logic-based modeling has enhanced our understanding and…
We study multivariate integration of functions that are invariant under the permutation (of a subset) of their arguments. Recently, in Nuyens, Suryanarayana, and Weimar (Adv. Comput. Math. (2016), 42(1):55--84), the authors derived an upper…
Classification of Non-linear Boolean functions is a long-standing problem in the area of theoretical computer science. In this paper, effort has been made to achieve a systematic classification of all n-variable Boolean functions, where…
In this paper, we present a construction of linear codes over $\f_{2^t}$ from Boolean functions, which is a generalization of Ding's method \cite[Theorem 9]{Ding15}. Based on this construction, we give two classes of linear codes…
Boolean functions can be represented in many ways including logical forms, truth tables, and polynomials. Additionally, Boolean functions have different canonical representations such as minimal disjunctive normal forms. Other canonical…
Analyzing the behavior of cryptographic functions in stripped binaries is a challenging but essential task. Cryptographic algorithms exhibit greater logical complexity compared to typical code, yet their analysis is unavoidable in areas…
Systems of Boolean equations of low degree arise in a natural way when analyzing block ciphers. The cipher's round functions relate the secret key to auxiliary variables that are introduced by each successive round. In algebraic…
Simulating a cellular automaton (CA) for t time-steps into the future requires t^2 serial computation steps or t parallel ones. However, certain CAs based on an Abelian group, such as addition mod 2, are termed ``linear'' because they obey…
Elementary cellular automata (ECA) are one-dimensional discrete models of computation with a small memory set that have gained significant interest since the pioneer work of Stephen Wolfram, who studied them as time-discrete dynamical…
We study functional clones, which are sets of non-negative pseudo-Boolean functions (functions $\{0,1\}^k\to\mathbb{R}_{\geq 0}$) closed under (essentially) multiplication, summation and limits. Functional clones naturally form a lattice…
We consider estimation in a particular semiparametric regression model for the mean of a counting process with ``panel count'' data. The basic model assumption is that the conditional mean function of the counting process is of the form…
The use of buried dopants to construct quantum-dot cellular automata is investigated as an alternative to conventional electronic devices for information transport and elementary computation. This provides a limit in terms of…
While model selection is a well-studied topic in parametric and nonparametric regression or density estimation, selection of possibly high-dimensional nuisance parameters in semiparametric problems is far less developed. In this paper, we…