Automata in SageMath---Combinatorics meet Theoretical Computer Science

TL;DR

This paper introduces a new finite state machine package in SageMath, demonstrating its application to combinatorial problems and automata-based solutions, including novel asymptotic digit expansion analysis.

Contribution

It presents a new SageMath package for automata and applies it to solve previously unknown combinatorial and digit expansion problems.

Findings

Computed the asymptotic Hamming weight of a digit expansion

Modeled digit problems using automata and transducers

Demonstrated SageMath's automata capabilities with examples

Abstract

The new finite state machine package in the mathematics software system SageMath is presented and illustrated by many examples. Several combinatorial problems, in particular digit problems, are introduced, modeled by automata and transducers and solved using SageMath. In particular, we compute the asymptotic Hamming weight of a non-adjacent-form-like digit expansion, which was not known before.