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cs.FL2026
The Finiteness Problem for Automaton Semigroups of Extended Bounded Activity
Daniele D'Angeli, Emanuele Rodaro, Jan Philipp Wächter
We extend the notion of activity for automaton semigroups and monoids introduced by Bartholdi, Godin, Klimann and Picantin to a more general setting. Their activity notion was alre…
cs.FL2026
The hereditariness problem for the Äerný conjecture
Emanuele Rodaro, Riccardo Venturi
This paper addresses the lifting problem for the Äerný conjecture: namely, whether the validity of the conjecture for a quotient automaton can always be transferred (or "lifted")…
cs.FL2025
The Freeness Problem for Automaton Semigroups
Daniele D'Angeli, Emanuele Rodaro, Jan Philipp Wächter
We show that the freeness problems for automaton semigroups and for automaton monoids are undecidable and, thereby, solve an open problem listed by Grigorchuk, Nekrashevych and Sus…