Automatic logarithm and associated measures

• Datum: 2023
• Hauptverfasser: Grigorchuk, R., Kogan, R., Vorobets, Y.
• Format: Artikel
• Sprache: English
• Veröffentlicht: Lugansk National Taras Shevchenko University 2023
• Schlagworte: Mealy automaton; Moore machine; regular rooted tree; Markov measure; finite-state measure; 20E08; 37B10; 60B05; 68Q45
• Online Zugang: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2014
• Назва журналу: Algebra and Discrete Mathematics

We introduce the notion of the automatic logarithm \(\operatorname{Log}_{\mathcal A}(\mathcal B)\) of a finite initial Mealy automaton \(\mathcal B\), with another automaton \(\mathcal A\) as the base. It allows one to find for any input word \(w\) a power \(n\) such that \(\mathcal B(w)=\mathcal A^...