45 citations · 158 across the 57 of their papers we have counts for
18 papers · 1 filter
Conjugacy problems in higher-dimensional Thompson groups
Ville Salo
We prove that topological conjugacy of elements of the Brin--Thompson group is undecidable for every . From a Turing machine , the reduction produces two elements o…
On the growth of actions of free products
Adrien Le Boudec, Nicolás Matte Bon, Ville Salo
If is a finitely generated group and a -set, the growth of the action of on is the function that measures the largest cardinality of a ball of radius in the…
Wreath products in the automorphism group of a full shift
Ville Salo
We prove that if a subgroup of the automorphism group $\Aut(Σ^\Z)$ of a non-trivial full shift acts on points of finite support (= points bi-asymptotic to a fixed point) with a…
The group of reversible Turing machines: subgroups, generators and computability
Sebastián Barbieri, Jarkko Kari, Ville Salo
We study an abstract group of reversible Turing machines. In our model, each machine is interpreted as a homeomorphism over a space which represents a tape filled with symbols and…
Distortion element in the automorphism group of a full shift
Antonin Callard, Ville Salo
We show that there is a distortion element in a finitely-generated subgroup of the automorphism group of the full shift, namely an element of infinite order whose word norm gro…
Thompson's in MCG of mixing SFT by PW-linear homeos
Ville Salo
In a recent paper, we showed that groups admitting "veelike actions" on a finite language embed in mapping class groups of certain two-sided subshifts. In this note, we illustrate…
Self-simulable groups
Sebastián Barbieri, Mathieu Sablik, Ville Salo
We say that a finitely generated group is self-simulable if every effectively closed action of on a closed subset of is the topolog…
Veelike actions and the MCG of a mixing SFT
Ville Salo
We embed Thompson's group in the mapping class group of a mixing subshift of finite type. Question~6.3 in [Boyle-Chuysurichay, 17] asks whether these mapping class groups are s…
Graph and wreath products in topological full groups of full shifts
Ville Salo
We prove that the topological full group of a two-sided full shift contains every right-angled Artin group (also called a graph group). More generally,…
Graph and wreath products of cellular automata
Ville Salo
We prove that the set of subgroups of the automorphism group of a two-sided full shift is closed under countable graph products. We introduce the notion of a group action without $…
Conjugacy of reversible cellular automata and one-head machines
Ville Salo
We show that conjugacy of reversible cellular automata is undecidable, whether the conjugacy is to be performed by another reversible cellular automaton or by a general homeomorphi…
Examples of Non-Busemann Horoballs
Ville Salo
In the f.g. setting, we construct horoballs which are "not centered around a geodesic" for generalized Heisenberg groups and all wreath products with an infinite acting group. That…
Universal CA groups with few generators
Ville Salo
There exist f.g.-universal cellular automata groups which are quotients of or , as previously conjectured by…
Alternation diameter of a product object
Ville Salo
We prove that every permutation of a Cartesian product of two finite sets can be written as a composition of three permutations, the first of which only modifies the left projectio…
Universal gates with wires in a row
Ville Salo
We give some optimal size generating sets for the group generated by shifts and local permutations on the binary full shift. We show that a single generator, namely the fully async…
Universal groups of cellular automata
Ville Salo
We prove that the group of reversible cellular automata (RCA), on any alphabet , contains a subgroup generated by three involutions which contains an isomorphic copy of every fi…
When are group shifts of finite type?
Ville Salo
It is known that a group shift on a polycyclic group is necessarily of finite type. We show that, for trivial reasons, if a group does not satisfy the maximal condition on subgroup…
The group of reversible Turing machines
Sebastián Barbieri, Jarkko Kari, Ville Salo
We consider Turing machines as actions over configurations in which only change them locally around a marked position that can move and carry a particular state.…