7 papers
Around Gromov's injectivity lemma and applications to post-injunctive groups
Xuan Kien Phung
Gottschalk's surjunctivity conjecture states that for all group universes and finite alphabets, every equivariant and continuous selfmap of the full shift, known as cellular automa…
Efficient space reduction techniques by optimized majority rules for the Kemeny aggregation problem and beyond
Xuan Kien Phung, Sylvie Hamel
The Kemeny aggregation problem consists of computing the consensus rankings of an election with respect to the well-known Kemeny-Young voting method. These consensus rankings satis…
On Gottschalk's surjunctivity conjecture for non-uniform cellular automata
Xuan Kien Phung
Gottschalk's surjunctivity conjecture for a group states that it is impossible for cellular automata (CA) over the universe with finite alphabet to produce strict embedding…
Topological stability of semigroup actions and shadowing
Tullio Ceccherini-Silberstein, Michel Coornaert, Xuan Kien Phung
We investigate expansiveness, topological stability, and shadowing for continuous actions of semigroups on compact Hausdorff spaces. We characterize semigroups for which all full s…
Strongly sofic monoids, sofic topological entropy, and surjunctivity
Tullio Ceccherini-Silberstein, Michel Coornaert, Xuan Kien Phung
We introduce the class of strongly sofic monoids. This class of monoids strictly contains the class of sofic groups and is a proper subclass of the class of sofic monoids. We defin…
Stable finiteness of monoid algebras and surjunctivity
Tullio Ceccherini-Silberstein, Michel Coornaert, Xuan Kien Phung
A monoid is said to be surjunctive if every injective cellular automaton with finite alphabet over is surjective. We show that monoid algebras of surjunctive monoids are st…