Representing Real Numbers in a Generalized Numeration Systems
Charlier Emilie, Le Gonidec Marion, Rigo Michel
TL;DR
This paper introduces a generalized framework for representing real numbers using abstract numeration systems based on non-regular languages, including applications to Dyck languages and rational base systems.
Contribution
It develops a novel approach to real number representation that extends beyond regular languages, enabling new applications in various numeration systems.
Findings
Framework applicable to non-regular languages like Dyck language
Representation of real numbers in rational base systems
Extension of numeration systems beyond traditional regular languages
Abstract
We show how to represent an interval of real numbers in an abstract numeration system built on a language that is not necessarily regular. As an application, we consider representations of real numbers using the Dyck language. We also show that our framework can be applied to the rational base numeration systems.
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Taxonomy
Topicssemigroups and automata theory · Logic, programming, and type systems · Computability, Logic, AI Algorithms