Related papers: Numeration systems without a dominant root and reg…
A variety of logical frameworks support the use of higher-order abstract syntax (HOAS) in representing formal systems. Although these systems seem superficially the same, they differ in a variety of ways; for example, how they handle a…
Chinese input recommendation plays an important role in alleviating human cost in typing Chinese words, especially in the scenario of mobile applications. The fundamental problem is to predict the conditional probability of the next word…
How might an advanced alien civilization manipulate the orbits within a planetary system to create a durable signpost that communicates its existence? While it is still debated whether such a purposeful advertisement would be prudent and…
In this Letter we identify special systems of (an arbitrary number) N of first-order Ordinary Differential Equations with homogeneous polynomials of arbitrary degree M on their right-hand sides, which feature very simple explicit solutions;…
This survey provides a comprehensive overview of the study of the binary and Boolean rank from both a mathematical and a computational perspective, with particular emphasis on their relationship to the real rank. We review the basic…
Many different systems with explicit substitutions have been proposed to implement a large class of higher-order languages. Motivations and challenges that guided the development of such calculi in functional frameworks are surveyed in the…
While recent work has begun to uncover the internal strategies that Large Language Models (LLMs) employ for simple arithmetic tasks, a unified understanding of their underlying mechanisms is still lacking. We extend recent findings showing…
We introduce a new concept of rank - relative rank associated to a filtered collection of polynomials. When the filtration is trivial our relative rank coincides with Schmidt rank (also called strength). We also introduce the notion of…
We study substitutive systems generated by nonprimitive substitutions and show that transitive subsystems of substitutive systems are substitutive. As an application we obtain a complete characterisation of the sets of words that can appear…
From a root system, one may consider the arrangement of reflecting hyperplanes, as well as its toric and elliptic analogues. The corresponding Weyl group acts on the complement of the arrangement and hence on its cohomology. We consider a…
This article provides a brief overview on a range of basic dynamical systems that conform to the logarithmic distribution of significant digits known as Benford's law. As presented here, most theorems are special cases of known, more…
We study combinatorial configurations with the associated point and line graphs being strongly regular. Examples not belonging to known classes such as partial geometries and their generalizations or elliptic semiplanes are constructed.…
In most introductory numerical analysis textbooks, the treatment of a single nonlinear equation often consists of a collection of all-purpose methods that frequently do not work or are inefficient. These textbooks neglect to teach the…
Non-classical generalizations of classical modal logic have been developed in the contexts of constructive mathematics and natural language semantics. In this paper, we discuss a general approach to the semantics of non-classical modal…
Several types of term rewriting systems can be distinguished by the way their rules overlap. In particular, we define the classes of prefix, suffix, bottom-up and top-down systems, which generalize similar classes on words. Our aim is to…
In order to work with mathematical content in computer systems, it is necessary to represent it in formal languages. Ideally, these are supported by tools that verify the correctness of the content, allow computing with it, and produce…
We introduce a new class of "random" subsets of natural numbers, WM sets. This class contains normal sets (sets whose characteristic function is a normal binary sequence). We establish necessary and sufficient conditions for solvability of…
We extend the well-known Dumont--Thomas numeration systems to $\mathbb{Z}$ using an approach inspired by the two's complement numeration system. Integers in $\mathbb{Z}$ are canonically represented by a finite word (starting with…
We study two positional numeration systems which are known for allowing very efficient addition and multiplication of complex numbers. The first one uses the base $\beta = \imath - 1$ and the digit set $\mathcal{D} = \{ 0, \pm 1, \pm \imath…
A hyperplane arrangement is said to satisfy the ``Riemann hypothesis'' if all roots of its characteristic polynomial have the same real part. This property was conjectured by Postnikov and Stanley for certain families of arrangements which…