Van Trung Pham

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Sand Pile Models are discrete dynamical systems emphasizing the phenomenon of Self-Organized Criticality. From a configuration composed of a finite number of stacked grains, we apply on every possible positions (in parallel) two grain moving transition rules. The transition rules permit one grain to fall to its right or left (symmetric) neighboring column(More)
It is well-known that the class of lattices generated by Chip Firing games (CFGs) is strictly included in the class of upper locally distributive lattices (ULD). However a necessary and sufficient criterion for this class is still an open question. In this paper we settle this problem by giving such a criterion. This criterion provides a polynomial-time(More)
This paper presents a generalization of the sandpile model, called the parallel symmetric sandpile model, which inherits the rule of the symmetric sandpile model and implements them in parallel. We prove that although the parallel model produces really less number of fixed points than that by the sequential model, the forms of fixed points of the two models(More)
Let (L;C ) be the (up to isomorphism unique) countable homogeneous structure carrying a binary branching C-relation. We study the reducts of (L;C ), i.e., the structures with domain L that are first-order definable in (L;C ). We show that up to existential interdefinability, there are finitely many such reducts. This implies that there are finitely many(More)
The Chip-firing game is a discrete dynamical system played on a graph, in which chips move along edges according to a simple local rule. Properties of the underlying graph are of course useful to the understanding of the game, but since a conjecture of Biggs that was proved by Merino López, we also know that the study of the Chip-firing game can give(More)
There exist two conjectures for constraint satisfaction problems (CSPs) of reducts of finitely bounded homogeneous structures: the first one states that tractability of the CSP of such a structure is, when the structure is a model-complete core, equivalent to its polymorphism clone satisfying a certain non-trivial linear identity modulo outer embeddings.(More)