Related papers: On Non-standard Models of Arithmetic with Uncounta…
In this paper, we discuss questions related to the renormalizability of the classical statistical approximation, an approximation scheme that has been used recently in several studies of out-of-equilibrium problems in Quantum Field Theory.…
Analog computation is an alternative to digital computation, that has recently re-gained prominence, since it includes neural networks and neuromorphic computing. Further important examples are cellular automata and differential analyzers.…
Non-forking is one of the most important notions in modern model theory capturing the idea of a generic extension of a type (which is a far-reaching generalization of the concept of a generic point of a variety). To a countable first-order…
The notion of surreal number was introduced by J.H. Conway in the mid 1970's: the surreal numbers constitute a linearly ordered (proper) class $No$ containing the class of all ordinal numbers ($On$) that, working within the background set…
Motivated by the problem of the existence of bounds on degrees and orders in checking primality of radical (partial) differential ideals, the nonstandard methods of van den Dries and Schmidt ["Bounds in the theory of polynomial rings over…
Science and mathematics help people better to understand world, eliminating different fallacies and misconceptions. One of such misconception is related to arithmetic, which is so important both for science and everyday life. People think…
Describing complex objects by elementary ones is a common strategy in mathematics and science in general. In their seminal 1965 paper, Kenneth Krohn and John Rhodes showed that every finite deterministic automaton can be represented (or…
Decidability of the problems of unboundedness and simultaneous unboundedness (aka. the diagonal problem) for higher-order recursion schemes was established by Clemente, Parys, Salvati, and Walukiewicz (2016). Then a procedure of optimal…
To enable the study of open sets in computational approaches to mathematics, lots of extra data and structure on these sets is assumed. For both foundational and mathematical reasons, it is then a natural question, and the subject of this…
Kleene Algebra with Tests (KAT) provides an elegant algebraic framework for describing non-deterministic finite-state computations. Using a small finite set of non-deterministic programming constructs (sequencing, non-deterministic choice,…
The paper deals with the following system of nonlinear difference equations \begin{equation*} x_{n+1}=ax_{n}^{2}y_{n}+bx_{n}y_{n}^{2},\ y_{n+1}=cx_{n}^{2}y_{n}+dx_{n}y_{n}^{2},\ n\in \mathbb{N}_{0}, \end{equation*} where the initial values…
Abstract numeration systems encode natural numbers using radix ordered words of an infinite regular language and linear recurrence sequences play a key role in their valuation. Sequence automata, which are deterministic finite automata with…
We reformulate a fundamental result due to Cook, Harbourne, Migliore and Nagel on the existence and irreduciblity of unexpected plane curves of a set of points $Z$ in $\mathbb{P}^2$, using the minimal degree of a Jacobian syzygy of the…
The lambda calculus is a universal programming language. It can represent the computable functions, and such offers a formal counterpart to the point of view of functions as rules. Terms represent functions and this allows for the…
Random access codes are an intriguing class of communication tasks that reveal an operational and quantitative difference between classical and quantum information processing. We formulate a natural generalization of random access codes and…
This work presents an empirical analysis of exact algorithms for the unbounded knapsack problem, which includes seven algorithms from the literature, two commercial solvers, and more than ten thousand instances. The terminating step-off, a…
Common definitions of the "standard" LOCAL model tend to be sloppy and even self-contradictory on one point: do the nodes update their state using an arbitrary function or a computable function? So far, this distinction has been safe to…
We indicate a way of distinguishing between structures, for which, we call two structures distinguishable. Roughly, being distinguishable means that they differ in the number of realizations each gives for some formula. Being…
In one-dimensional Diophantine approximation, the Diophantine properties of a real number are characterized by its partial quotients, especially the growth of its large partial quotients. Notably, Kleinbock and Wadleigh [Proc. Amer. Math.…
Working in the Blum-Shub-Smale model of computation on the real numbers, we answer several questions of Meer and Ziegler. First, we show that, for each natural number d, an oracle for the set of algebraic real numbers of degree at most d is…