Related papers: Representing Real Numbers in a Generalized Numerat…
In the present paper we explore a way to represent numbers with respect to the base $-\frac32$ using the set of digits $\{0,1,2\}$. Although this number system shares several properties with the classical decimal system, it shows remarkable…
The work is devoted to the development of numerical methods for computing "formal solutions" of interval systems of linear algebraic equations. These solutions are found in Kaucher interval arithmetic, which extends and completes the…
We survey facts mostly emerging from the seminal results of Alan Cobham obtained in the late sixties and early seventies. We do not attempt to be exhaustive but try instead to give some personal interpretations and some research directions.…
Formal languages are sets of strings of symbols described by a set of rules specific to them. In this note, we discuss a certain class of formal languages, called regular languages, and put forward some elementary results. The properties of…
Number systems with a rational number $a/b > 1$ as base have gained interest in recent years. In particular, relations to Mahler's 3/2-problem as well as the Josephus problem have been established. In the present paper we show that the…
Let L be an infinite regular language on a totally ordered alphabet (A,<). Feeding a finite deterministic automaton (with output) with the words of L enumerated lexicographically with respect to < leads to an infinite sequence over the…
We present a comprehensive survey of constructions of the real numbers (from either the rationals or the integers) in a unified fashion, thus providing an overview of most (if not all) known constructions ranging from the earliest attempts…
In this paper we present an alternative approach to formalize the theory of logic programming. In this formalization we allow existential quantified variables and equations in queries. In opposite to standard approaches the role of answer…
We discuss a formal system of mathematics. We use it to construct the natural numbers.
Discrete mathematics is the foundation of computer science. It focuses on concepts and reasoning methods that are studied using math notations. It has long been argued that discrete math is better taught with programming, which takes…
In this paper, we develop a representation-theoretic formulation of discrete-time linear systems. We show that such systems are naturally viewed as representations of time groups acting on vector spaces, thereby endowing the state space…
Formalizing syntactic proofs of properties of logics, programming languages, security protocols, and other formal systems is a significant challenge, in large part because of the obligation to handle name-binding correctly. We present an…
Given a rational elliptic surface X over an algebraically closed field, we investigate whether a given natural number k can be the intersection number of two sections of X. If not, we say that k a gap number. We try to answer when gap…
We study the computational complexity of converting one representation of real numbers into another representation. Typical examples of representations are Cauchy sequences, base-10 expansions, Dedekind cuts and continued fractions.
This paper presents a new numerical abstract domain for static analysis by abstract interpretation. This domain allows us to represent invariants of the form (x-y<=c) and (+/-x<=c), where x and y are variables values and c is an integer or…
This paper focuses on greedy expansions, one possible representation of numbers, and on arithmetical operations with them. Performing addition or multiplication some additional digits can appear. We study bounds on the number of such digits…
In this paper, we develop an explicit method to express finite algebraic numbers (in particular, certain idempotents among them) in terms of linear recurrent sequences, and give applications to the characterization of the splitting primes…
We propose a formalism for representation of finite languages, referred to as the class of IDL-expressions, which combines concepts that were only considered in isolation in existing formalisms. The suggested applications are in natural…
Recently uncovered second derivative discontinuous solutions of the simplest linear ordinary differential equation define not only an nonstandard extension of the framework of the ordinary calculus, but also provide a dynamical…
Mathematical language in scientific communications and educational scenarios is important yet relatively understudied compared to natural languages. Recent works on mathematical language focus either on representing stand-alone mathematical…