5 papers
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…
Context-Free Trees
Jan Philipp Wächter
Muller and Schupp introduced the concept of context-free graphs (originating from Cayley graphs of context-free groups). These graphs are always tree-like (i.e. quasi-isometric to…
Preserving self-similarity in free products of semigroups
Tara Macalister Brough, Jan Philipp Wächter, Janette Welker
We improve on earlier results on the closure under free products of the class of automaton semigroups. We consider partial automata and show that the free product of two self-simil…
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…
Equations in wreath products
Laurent Bartholdi, Ruiwen Dong, Leon Pernak +1
We survey solvability of equations in wreath products of groups, and prove that the quadratic diophantine problem is solvable in wreath products of Abelian groups. We consider the…