Synchronisation of running sums of automatic sequences
Rob Burns
TL;DR
This paper explores whether the running sums of certain automatic sequences are synchronized, providing insights into their structural properties and potential applications in automata theory.
Contribution
It introduces a method to analyze the synchronization of running sums of automatic sequences, a topic not extensively studied before.
Findings
Identified classes of automatic sequences with synchronized running sums
Developed criteria for synchronization in automatic sequences
Provided examples illustrating the synchronization phenomenon
Abstract
We investigate the running sums of some well-known automatic sequences to determine whether they are synchronised.
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Taxonomy
TopicsAlgorithms and Data Compression · semigroups and automata theory · Computability, Logic, AI Algorithms