Related papers: Constructing Boolean Functions With Potential Opti…
We give a definition of some classes of boolean algebras generalizing free boolean algebras; they satisfy a universal property that certain functions extend to homomorphisms. We give a combinatorial property of generating sets of these…
We determine all composition-closed equational classes of Boolean functions. These classes provide a natural generalization of clones and iterative algebras: they are closed under composition, permutation and identification…
Physical Unclonable Functions evaluate manufacturing variations to generate secure cryptographic keys for embedded systems without secure key storage. It is explained how methods from coding theory are applied in order to ensure reliable…
Counting functions are constructed for sums of integers raised to a fixed positive rational power. That is, given values formed by $u_1^{j/k} + u_2^{j/k} + ... + u_l^{j/k}$, $u_i \in \mathbb{Z}^+$, the number of values less than or equal to…
In automated complexity analysis, noninterference-based type systems statically guarantee, via soundness, the property that well-typed programs compute functions of a given complexity class, e.g., the class FP of functions computable in…
In this paper, an algebraic binning based coding scheme and its associated achievable rate for key generation using physically unclonable functions (PUFs) is determined. This achievable rate is shown to be optimal under the generated-secret…
Many underlying structural and functional factors that determine the fault behavior of a combinational network, are not yet fully understood. In this paper, we show that there exists a large class of Boolean functions, called root…
Selman and Kautz's work on ``knowledge compilation'' established how approximation (strengthening and/or weakening) of a propositional knowledge-base can be used to speed up query processing, at the expense of completeness. In this…
Dillon-like Boolean functions are known, in the literature, to be those trace polynomial functions from $\mathbb{F}_{2^{2n}}$ to $\mathbb{F}_{2}$, with all the exponents being multiples of $2^n-1$ often called Dillon-like exponents. This…
Performing an additive decomposition of arbitrary functions of random elements is paramount for global sensitivity analysis and, therefore, the interpretation of black-box models. The well-known seminal work of Hoeffding characterized the…
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…
For positive integers d, r, and M, we consider the class of rational functions on real d-dimensional space whose denominators are products of at most r functions of the form 1+Q(x) where each Q is a quadratic form with eigenvalues bounded…
We study numerically the ODE/IM correspondence for untwisted affine Lie algebras associated with simple Lie algebras including exceptional type. We consider the linear problem obtained from the massless limit of that of the modified affine…
Jayne and Rogers proved that every function from an analytic space into a separable metric space is decomposable into countably many continuous functions with closed domains if and only if the preimage of each $F_\sigma$ set under it is…
In this paper, we give a theoretical analysis for the algorithms to compute functional decomposition for multivariate polynomials based on differentiation and homogenization which are proposed by Ye, Dai, Lam (1999) and Faug$\mu$ere, Perret…
We revisit and generalize our previous algebraic construction of the chiral effective action for Conformal Field Theory on higher genus Riemann surfaces. We show that the action functional can be obtained by evaluating a certain Deligne…
This paper studies the important problem of quantum classification of Boolean functions from a entirely novel perspective. Typically, quantum classification algorithms allow us to classify functions with a probability of $1.0$, if we are…
Function name prediction is crucial for understanding stripped binaries in software reverse engineering, a key step for \textbf{enabling subsequent vulnerability analysis and patching}. However, existing approaches often struggle with…
Propagation criterion of degree $l$ and order $k$ ($PC(l)$ of order $k$) and resiliency of vectorial Boolean functions are important for cryptographic purpose (see [1, 2, 3,6, 7,8,10,11,16]. Kurosawa, Stoh [8] and Carlet [1] gave a…
We show that the class of $\mathcal{L}$-constructible functions is closed under integration for any $P$-minimal expansion of a $p$-adic field $(K,\mathcal{L})$. This generalizes results previously known for semi-algebraic and sub-analytic…