Xuan Kien Phung

activity

20172026

most citedOn the Garden of Eden theorem for endomorphisms of symbolic algebraic varieties

14 citations · 77 across the 28 of their papers we have counts for

collaborators

31 papers

math.GR2026

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…

cs.DS2025

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…

math.DS2025

On Gottschalk's surjunctivity conjecture for non-uniform cellular automata

Xuan Kien Phung

Gottschalk's surjunctivity conjecture for a group $G$ states that it is impossible for cellular automata (CA) over the universe $G$ with finite alphabet to produce strict embedding…

math.DS2025

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…

math.GR2024

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…

math.RA2024

Stable finiteness of monoid algebras and surjunctivity

Tullio Ceccherini-Silberstein, Michel Coornaert, Xuan Kien Phung

A monoid $M$ is said to be surjunctive if every injective cellular automaton with finite alphabet over $M$ is surjective. We show that monoid algebras of surjunctive monoids are st…

math.DS2024★ 1 cited

Generalized Gottschalk's conjecture for sofic groups and applications

Xuan Kien Phung

We establish generalizations of the well-known surjunctivity theorem of Gromov and Weiss as well as the dual-surjunctivity theorem of Capobianco, Kari and Taati for cellular automa…

math.GR2023★ 1 cited

First-order model theory and Kaplansky's stable finiteness conjecture

Tullio Ceccherini-Silberstein, Michel Coornaert, Xuan Kien Phung

Using algebraic geometry methods, the third author proved that the group ring of a surjunctive group with coefficients in a field is always stably finite. In other words, every gro…

cs.DM2023

Space reduction techniques for the $3$ -wise Kemeny problem

Xuan Kien Phung, Sylvie Hamel

Kemeny's rule is one of the most studied and well-known voting schemes with various important applications in computational social choice and biology. Recently, Kemeny's rule was g…

cs.GT2023

Optimal majority rules and quantitative Condorcet properties of setwise Kemeny voting schemes

Xuan Kien Phung, Sylvie Hamel

The important Kemeny problem, which consists of computing median consensus rankings of an election with respect to the Kemeny voting rule, admits important applications in biology…

math.DS2023

On the Garden of Eden theorem for non-uniform cellular automata

Xuan Kien Phung

We establish several extensions of the well-known Garden of Eden theorem for non-uniform cellular automata over the full shifts and over amenable group universes. In particular, ou…

math.DS2022★ 1 cited

Some pointwise and decidable properties of non-uniform cellular automata

Xuan Kien Phung

For non-uniform cellular automata (NUCA) with finite memory over an arbitrary universe with multiple local transition rules, we show that pointwise nilpotency, pointwise periodicit…

math.DS2022★ 6 cited

Stable finiteness of twisted group rings and noisy linear cellular automata

Xuan Kien Phung

For linear non-uniform cellular automata (NUCA) which are local perturbations of linear CA over a group universe $G$ and a finite-dimensional vector space alphabet $V$ over an arbi…

math.DS2022★ 1 cited

On linear non-uniform cellular automata: duality and dynamics

Xuan Kien Phung

For linear non-uniform cellular automata (NUCA) over an arbitrary universe, we introduce and investigate their dual linear NUCA. Generalizing results for linear CA, we show that dy…

math.DS2022

On reversible asynchronous non-uniform cellular automata

Xuan Kien Phung

We study the class of asynchronous non-uniform cellular automata (ANUCA) over an arbitrary group universe with multiple local transition rules. We introduce the notion of stable in…

math.DS2021

On images of subshifts under injective morphisms of symbolic varieties

Xuan Kien Phung

We show that the image of a subshift $X$ under various injective morphisms of symbolic algebraic varieties over monoid universes with algebraic variety alphabets is a subshift of f…

math.AG2021

Weakly surjunctive groups and symbolic group varieties

Xuan Kien Phung

In this paper, we introduce the classes of weakly surjunctive and linearly surjunctive groups which include all sofic groups and more generally all surjunctive groups. We investiga…

math.AG2021★ 2 cited

LEF-groups and endomorphisms of symbolic varieties

Xuan Kien Phung

Let $G$ be a group and let $X$ be an algebraic variety over an algebraically closed field $k$ of characteristic zero. Denote $A = X (k)$ the set of rational points of $X$ . We investig…

math.AG2021

A geometric generalization of Kaplansky's direct finiteness conjecture

Xuan Kien Phung

Let $G$ be a group and let $k$ be a field. Kaplansky's direct finiteness conjecture states that every one-sided unit of the group ring $k [G]$ must be a two-sided unit. In this pape…

math.DS2021

On symbolic group varieties and dual surjunctivity

Xuan Kien Phung

Let $G$ be a group. Let $X$ be an algebraic group over an algebraically closed field $K$ . Denote by $A = X (K)$ the set of rational points of $X$ . We study algebraic group cellular au…

math.DS2020★ 14 cited

Shadowing for families of endomorphisms of generalized group shifts

Xuan Kien Phung

Let $G$ be a countable monoid and let $A$ be an Artinian group (resp. an Artinian module). Let $Σ \subset A^{G}$ be a closed subshift which is also a subgroup (resp. a submodule) of $…

math.GR2020

On dynamical finiteness properties of algebraic group shifts

Xuan Kien Phung

Let $G$ be a group and let $V$ be an algebraic group over an algebraically closed field. We introduce algebraic group subshifts $Σ \subset V^{G}$ which generalize both the class of al…

math.DS2020★ 12 cited

On linear shifts of finite type and their endomorphisms

Tullio Ceccherini-Silberstein, Michel Coornaert, Xuan Kien Phung

Let $G$ be a group and let $A$ be a finite-dimensional vector space over an arbitrary field $K$ . We study finiteness properties of linear subshifts $Σ \subset A^{G}$ and the dynamical…

math.DS2020★ 8 cited

Invariant sets and nilpotency of endomorphisms of algebraic sofic shifts

Tullio Ceccherini-Silberstein, Michel Coornaert, Xuan Kien Phung

Let $G$ be a group and let $V$ be an algebraic variety over an algebraically closed field $K$ . Let $A$ denote the set of $K$ -points of $V$ . We introduce algebraic sofic subshifts $…

Around Gromov's injectivity lemma and applications to post-injunctive groups

Efficient space reduction techniques by optimized majority rules for the Kemeny aggregation problem and beyond

On Gottschalk's surjunctivity conjecture for non-uniform cellular automata

Topological stability of semigroup actions and shadowing

Strongly sofic monoids, sofic topological entropy, and surjunctivity

Stable finiteness of monoid algebras and surjunctivity

Generalized Gottschalk's conjecture for sofic groups and applications

First-order model theory and Kaplansky's stable finiteness conjecture

Space reduction techniques for the 3-wise Kemeny problem

Optimal majority rules and quantitative Condorcet properties of setwise Kemeny voting schemes

On the Garden of Eden theorem for non-uniform cellular automata

Some pointwise and decidable properties of non-uniform cellular automata

Stable finiteness of twisted group rings and noisy linear cellular automata

On linear non-uniform cellular automata: duality and dynamics

On reversible asynchronous non-uniform cellular automata

On images of subshifts under injective morphisms of symbolic varieties

Weakly surjunctive groups and symbolic group varieties

LEF-groups and endomorphisms of symbolic varieties

A geometric generalization of Kaplansky's direct finiteness conjecture

On symbolic group varieties and dual surjunctivity

Shadowing for families of endomorphisms of generalized group shifts

On dynamical finiteness properties of algebraic group shifts

On linear shifts of finite type and their endomorphisms

Invariant sets and nilpotency of endomorphisms of algebraic sofic shifts

Space reduction techniques for the $3$ -wise Kemeny problem