Related papers: IDEM Enough? Evolving Highly Nonlinear Idempotent …
In this paper we develop the notion of ergodicity to include functions dominated by a weight $w$. Such functions have polynomial means and include, amongst many others, the $w$-almost periodic functions. This enables us to describe the…
We demonstrate under appropriate finiteness conditions that a coarse embedding induces an inequality of homological Dehn functions. Applications of the main results include a characterization of what finitely presentable groups may admit a…
Vectorial Boolean functions are crucial building-blocks in symmetric ciphers. Different known attacks on block ciphers have resulted in diverse cryptographic criteria for vectorial Boolean functions, such as differential uniformity and…
Recent work demonstrated the existence of Boolean functions for which Shapley values provide misleading information about the relative importance of features in rule-based explanations. Such misleading information was broadly categorized…
We present a conceptual framework for extending homomorphic encryption beyond arithmetic or Boolean operations into the domain of intuitionistic logic proofs and, by the Curry-Howard correspondence, into the domain of typed functional…
Boolean function bi-decomposition is ubiquitous in logic synthesis. It entails the decomposition of a Boolean function using two-input simple logic gates. Existing solutions for bi-decomposition are often based on BDDs and, more recently,…
This article makes the key observation that when using cylindrical algebraic decomposition (CAD) to solve a problem with respect to a set of polynomials, it is not always the signs of those polynomials that are of paramount importance but…
We study transnormal and isoparametric functions on closed Riemannian 4-manifolds and establish fundamental restrictions on their topology and geometry. In particular, we show that such manifolds cannot be endowed with negatively curved…
The effects of the finite size of the network on the evolutionary dynamics of a Boolean network are analyzed. In the model considered, Boolean networks evolve via a competition between nodes that punishes those in the majority. It is found…
In this paper, we show that an attempt to construct shape invariant extensions of a known shape invariant potential leads to, apart from a shift by a constant, the well known technique of isospectral shift deformation. Using this, we…
In this paper, we consider bounded width circuits and nondeterministic circuits in three somewhat new directions. In the first part of this paper, we mainly consider bounded width circuits. The main purpose of this part is to prove that…
This paper introduces a new functional expansion framework that extends classical ideas beyond the Taylor series. Unlike traditional Taylor expansions based on local polynomial approximations, the proposed approach arises from exact…
This paper presents a novel framework for high-dimensional nonlinear quantum computation that exploits tensor products of amplified vector and matrix encodings to efficiently evaluate multivariate polynomials. The approach enables the…
We examine a hierarchy of equivalence classes of quasi-random properties of Boolean Functions. In particular, we prove an equivalence between a number of properties including balanced influences, spectral discrepancy, local strong…
This paper is devoted to heuristic aspects of the so-called idempotent calculus. There is a correspondence between important, useful and interesting constructions and results over the field of real (or complex) numbers and similar…
A fuzzy Boolean function is a map $f:\cube^n\to [0,1]$, where $n\in\mathbb N$. We introduce and compare three ways of saying that such a function has bounded complexity. The first is a sampling property: the value $f(x)$ can be recovered,…
Basis functions which are invariant under the operations of a rotational point group $G$ are able to describe any 3-D object which exhibits the rotational point group symmetry. However, in order to characterize the spatial statistics of an…
In this paper, we study the value distributions of perfect nonlinear functions, i.e., we investigate the sizes of image and preimage sets. Using purely combinatorial tools, we develop a framework that deals with perfect nonlinear functions…
We present foundational work on standard bases over rings and on Boolean Groebner bases in the framework of Boolean functions. The research was motivated by our collaboration with electrical engineers and computer scientists on problems…
Bent functions as optimal combinatorial objects are difficult to characterize and construct. In the literature, bent idempotents are a special class of bent functions and few constructions have been presented, which are restricted by the…