14 citations · 77 across the 28 of their papers we have counts for
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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…
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…
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…
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…
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 and a finite-dimensional vector space alphabet over an arbi…
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…
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…
On images of subshifts under injective morphisms of symbolic varieties
Xuan Kien Phung
We show that the image of a subshift under various injective morphisms of symbolic algebraic varieties over monoid universes with algebraic variety alphabets is a subshift of f…
On symbolic group varieties and dual surjunctivity
Xuan Kien Phung
Let be a group. Let be an algebraic group over an algebraically closed field . Denote by the set of rational points of . We study algebraic group cellular au…
Shadowing for families of endomorphisms of generalized group shifts
Xuan Kien Phung
Let be a countable monoid and let be an Artinian group (resp. an Artinian module). Let be a closed subshift which is also a subgroup (resp. a submodule) of $…
On linear shifts of finite type and their endomorphisms
Tullio Ceccherini-Silberstein, Michel Coornaert, Xuan Kien Phung
Let be a group and let be a finite-dimensional vector space over an arbitrary field . We study finiteness properties of linear subshifts and the dynamical…
Invariant sets and nilpotency of endomorphisms of algebraic sofic shifts
Tullio Ceccherini-Silberstein, Michel Coornaert, Xuan Kien Phung
Let be a group and let be an algebraic variety over an algebraically closed field . Let denote the set of -points of . We introduce algebraic sofic subshifts $…
On sofic groups, Kaplansky's conjectures, and endomorphisms of pro-algebraic groups
Xuan Kien Phung
Let be a group. Let be a connected algebraic group over an algebraically closed field . Denote by the set of -points of . We study a class of endomorphism…
On the Garden of Eden theorem for endomorphisms of symbolic algebraic varieties
Tullio Ceccherini-Silberstein, Michel Coornaert, Xuan Kien Phung
Let be an amenable group and let be an irreducible complete algebraic variety over an algebraically closed field . Let denote the set of -points of and let $τ…