Related papers: A relation between additive and multiplicative com…
We prove a certain duality relation for orthogonal polynomials defined on a finite set. The result is used in a direct proof of the equivalence of two different ways of computing the correlation functions of a discrete orthogonal polynomial…
We consider a subclass of tilings, the tilings obtained by cut and projection. Under somewhat standard assumptions, we show that the natural complexity function has polynomial growth. We compute its exponent \alpha in terms of the ranks of…
We unify in a large class of additive functions the results obtained in the first part of this work. The proof rests on series involving the Riemann zeta function and certain sums of primes which may have their own interest.
We consider the problem of jointly minimizing forms of two Boolean functions $f, g \colon \{0,1\}^J \to \{0,1\}$ such that $f + g \leq 1$ and so as to separate disjoint sets $A \cup B \subseteq \{0,1\}^J$ such that $f(A) = \{1\}$ and $g(B)…
Among abelian extensions of a congruence function field, an asymptotic relation of class number and genus is established. The proof is classical, employing well-known results from congruence function field theory.
The associativity property, usually defined for binary functions, can be generalized to functions of a given fixed arity n>=1 as well as to functions of multiple arities. In this paper, we investigate these two generalizations in the case…
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…
We study the P versus NP problem through properties of functions and monoids, continuing the work of [3]. Here we consider inverse monoids whose properties and relationships determine whether P is different from NP, or whether injective…
We comment on recent results in the field of information based complexity, which state (in a number of different settings), that approximation of infinitely differentiable functions is intractable and suffers from the curse of…
Multiplication is one of the most fundamental computational problems, yet its true complexity remains elusive. The best known upper bound, by F\"{u}rer, shows that two $n$-bit numbers can be multiplied via a boolean circuit of size $O(n \lg…
This article presents an equivalent formulation of the implicit complementarity problem. We demonstrate that solution of the equivalent formulation is equivalent to the solution of the implicit complementarity problem. Moreover, we provide…
The addition relation for the Riemann theta functions and for its limits, which lead to the appearance of exponential functions in soliton type equations is discussed. The presented form of addition property resolves itself to the…
Functional equations satisfied by additive functions have a special interest not only in the theory of functional equations, but also in the theory of (commutative) algebra because the fundamental notions such as derivations and…
The theory of partition congruences has been a fascinating and difficult subject for over a century now. In attempting to prove a given congruence family, multiple possible complications include the genus of the underlying modular curve,…
We show conflict complexity of every total Boolean function, recently introduced in [Swagato Sanyal. A composition theorem via conict complexity. arXiv preprint arXiv:1801.03285, 2018.] to prove a composition theorem of randomized decision…
The approximate degree of a Boolean function $f(x_{1},x_{2},\ldots,x_{n})$ is the minimum degree of a real polynomial that approximates $f$ pointwise within $1/3$. Upper bounds on approximate degree have a variety of applications in…
V.I. Arnold has recently defined the complexity of finite sequences of zeroes and ones in terms of periods and preperiods of attractors of a dynamic system of the operator of finite differentiation. Arnold has set up a hypothesis that the…
The derivative expansion approach to the calculation of the interaction between two surfaces, is a generalization of the proximity force approximation, a technique of widespread use in different areas of physics. The derivative expansion…
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,…
Boolean networks are a general model of interacting entities, with applications to biological phenomena such as gene regulation. Attractors play a central role, and the schedule of entities update is a priori unknown. This article presents…