Cover Image

Using finite automata to compute the base-$b$ representation of the golden ratio and other quadratic irrationals

Fuente: arXiv

Saved in:

Bibliographic Details
Main Authors:	Barnoff, Aaron, Bright, Curtis, Shallit, Jeffrey
Format:	Preprint
Published:	2024
Subjects:	Formal Languages and Automata Theory Discrete Mathematics Number Theory
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

Similar Items

The Tribonacci constant and finite automata
by: Shallit, Jeffrey
Published: (2025)

Proving Properties of $φ$-Representations with the Walnut Theorem-Prover
by: Shallit, Jeffrey
Published: (2023)

An 'Experimental Mathematics' Approach to Stolarsky Interspersions via Automata Theory
by: Shallit, Jeffrey
Published: (2025)

Brik's sequence: a strange recursion
by: Shallit, Jeffrey
Published: (2026)

The Hurt-Sada Array and Zeckendorf Representations
by: Shallit, Jeffrey
Published: (2025)

Cloitre's Self-Generating Sequence
by: Shallit, Jeffrey
Published: (2025)

The Narayana Morphism and Related Words
by: Shallit, Jeffrey
Published: (2025)

Balanced Fibonacci word rectangles, and beyond
by: Shallit, Jeffrey, et al.
Published: (2025)

State Complexity of Shifts of the Fibonacci Word
by: Moradi, Delaram, et al.
Published: (2026)

Consecutive Power Occurrences in Sturmian Words
by: Bell, Jason, et al.
Published: (2024)

Complexity of Linear Subsequences of $k$-Automatic Sequences
by: Moradi, Delaram, et al.
Published: (2025)

Beatty Sequences for a Quadratic Irrational: Decidability and Applications
by: Schaeffer, Luke, et al.
Published: (2024)

Runs in Paperfolding Sequences
by: Shallit, Jeffrey
Published: (2024)

Ten Squares Force an Overlap
by: Shallit, Jeffrey
Published: (2026)

The Repetition Threshold for Rote Sequences
by: Ollinger, Nicolas, et al.
Published: (2024)

String Attractors for Automatic Sequences
by: Schaeffer, Luke, et al.
Published: (2020)

Some Fibonacci-Related Sequences
by: Cloitre, Benoit, et al.
Published: (2023)

Strongly k-recursive sequences
by: Krenn, Daniel, et al.
Published: (2024)

Self-Verifying Predicates in Büchi Arithmetic
by: Khodier, Mazen, et al.
Published: (2025)

Dyck Words, Pattern Avoidance, and Automatic Sequences
by: Mol, Lucas, et al.
Published: (2023)

Some Remarks on Palindromic Periodicities
by: Fici, Gabriele, et al.
Published: (2024)

Complexity of Linear Subsequences of Fibonacci-Automatic Sequences
by: Moradi, Delaram, et al.
Published: (2026)

Pseudoperiodic Words and a Question of Shevelev
by: Meleshko, Joseph, et al.
Published: (2022)

Antisquares and Critical Exponents
by: Baranwal, Aseem, et al.
Published: (2022)

Repetition Threshold for Binary Automatic Sequences
by: Allouche, J. -P., et al.
Published: (2024)

New properties of the $φ$-representation of integers
by: Shallit, Jeffrey, et al.
Published: (2025)

Counting Polyominoes in a Rectangle b x h
by: Marin, Louis
Published: (2024)

Topological transitivity of group cellular automata is decidable
by: Castronuovo, Niccolò, et al.
Published: (2026)

On finite extensions of lamplighter groups
by: Bodart, Corentin
Published: (2025)

Modular Decomposition of Hierarchical Finite State Machines
by: Biggar, Oliver, et al.
Published: (2021)

Decidability and Characterization of Expansivity for Group Cellular Automata
by: Castronuovo, Niccolo', et al.
Published: (2025)

Algebraic Characterization of Reversible First Degree Cellular Automata over $\mathbb{Z}_d$
by: J., Baby C., et al.
Published: (2026)

A Divide and Conquer Algorithm for Deciding Group Cellular Automata Dynamics
by: Castronuovo, Niccolo', et al.
Published: (2025)

Persistent Permutability in Choice Petri Nets
by: Best, Eike, et al.
Published: (2026)

A New Notion of Regularity: Finite State Automata Accepting Graphs
by: Meeres, Yvo Ad
Published: (2024)

Differential Tree Automata
by: Manssour, Rida Ait El, et al.
Published: (2024)

Self-descriptive Sequences directed by two Periodic Sequences
by: Akiyama, Shigeki, et al.
Published: (2024)

Membership problems in nilpotent groups
by: Bodart, Corentin
Published: (2024)

Bounded Generation of Submonoids of Heisenberg Groups
by: Shafrir, Doron
Published: (2024)

One Adaptive Trailing Head Can Outperform Many Oblivious Trailing Heads
by: Cruz, Julianne, et al.
Published: (2026)