7 citations · 17 across the 12 of their papers we have counts for
6 papers · 1 filter
A linear bound for the size of the finite terminal assembly of a directed non-cooperative tile assembly system
Sergiu Ivanov, Damien Regnault
The abstract tile assembly model (aTam) is a model of DNA self-assembly. Most of the studies focus on cooperative aTAM where a form of synchronization between the tiles is possible…
On the directed tile assembly systems at temperature 1
Pierre-Étienne Meunier, Damien Regnault
We show here that a model called directed self-assembly at temperature 1 is unable to do complex computations like the ones of a Turing machine. Since this model can be seen as a g…
The program-size complexity of self-assembled paths
Pierre-Étienne Meunier, Damien Regnault, Damien Woods
We prove a Pumping Lemma for the noncooperative abstract Tile Assembly Model, a model central to the theory of algorithmic self-assembly since the beginning of the field. This theo…
Non-cooperatively assembling large structures: a 2D pumping lemma cannot be as powerful as its 1D counterpart
Pierre-Etienne Meunier, Damien Regnault
We show the first asymptotically efficient constructions in the so-called "noncooperative planar tile assembly" model. Algorithmic self-assembly is the study of the local, distribu…
A pumping lemma for non-cooperative self-assembly
Pierre-Étienne Meunier, Damien Regnault
We prove a result which strongly hints at the computational weakness of a model of tile assembly that has so far resisted many attempts of formal analysis or positive constructions…
A pumping lemma for non-cooperative self-assembly
Pierre-Étienne Meunier, Damien Regnault
We prove the computational weakness of a model of tile assembly that has so far resisted many attempts of formal analysis or positive constructions. Specifically, we prove that, in…