The Self-Similarity of Free Semigroups and Groups
Emanuele Rodaro, Jan Philipp W\"achter
TL;DR
This paper surveys the current state of research on self-similar and automaton representations of free groups and semigroups, highlighting key results, open problems, and algebraic decision issues.
Contribution
It provides a comprehensive overview of known results and open questions in the area of self-similar structures and automaton presentations of free algebraic objects.
Findings
Summary of key results on self-similar free groups and semigroups
Discussion of open problems in automaton presentations
Analysis of algebraic decision problems related to these structures
Abstract
We give a survey on results regarding self-similar and automaton presentations of free groups and semigroups and related products. Furthermore, we discuss open problems and results with respect to algebraic decision problems in this area.
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Taxonomy
Topicssemigroups and automata theory · Geometric and Algebraic Topology · Mathematical Dynamics and Fractals