Related papers: Two-dimensional tile displacement can simulate cel…
The early promises of DNA computing to deliver a massively parallel architecture well-suited to computationally hard problems have so far been largely unkept. Indeed, it is probably fair to say that only toy problems have been addressed…
DNA origami is a widely used method to construct nanostructures by self-assembling designed DNA strands. These structures are often used as "pegboards" for templated assembly of proteins, gold nanoparticles, aptamers, and other molecules,…
We investigate the role of nondeterminism in Winfree's abstract Tile Assembly Model (aTAM), which was conceived to model artificial molecular self-assembling systems constructed from DNA. Of particular practical importance is to find tile…
We investigate the computing power of a restricted class of DNA strand displacement structures: those that are made of double strands with nicks (interruptions) in the top strand. To preserve this structural invariant, we impose…
We show that the Tile Assembly Model exhibits a strong notion of universality where the goal is to give a single tile assembly system that simulates the behavior of any other tile assembly system. We give a tile assembly system that is…
We study the computational power of the Full-Tilt model of motion planning, where slidable polyominos are moved maximally around a board by way of a sequence of directional ``tilts.'' We focus on the deterministic scenario in which the…
The objective is to find a Cellular Automata rule that can form a 2D point pattern with a maximum number of points (1-cells). Points are not allowed to touch each other, they have to be separated by 0-cells, and every 0-cell can find at…
Winfree's abstract Tile Assembly Model (aTAM) is a model of molecular self-assembly of DNA complexes known as tiles, which float freely in solution and attach one at a time to a growing "seed" assembly based on specific binding sites on…
We study a coarse-graining procedure for quantum cellular automata on hypercubic lattices that consists in grouping neighboring cells into tiles and selecting a subspace within each tile. This is done in such a way that multiple evolution…
Molecular-scale computation is crucial for smart materials and nanoscale devices, yet creating single-molecule systems capable of complex computations remains challenging. We present a theoretical framework for a single-molecule computer…
In a probabilistic cellular automaton in which all local transitions have positive probability, the problem of keeping a bit of information indefinitely is nontrivial, even in an infinite automaton. Still, there is a solution in 2…
DNA origami consists of a long scaffold strand and short staple strands that self-assemble into a target 2D or 3D shape. It is a widely used construct in nucleic acid nanotechnology, offering a cost-effective way to design and create…
DNA nanostructures are made using synthetic DNA strands, the sequences of which are designed such that they will self-assemble into the desired form by hybridization of complementary domains. Various structures and devices have been…
One-dimensional cellular automata are discrete dynamical systems that operate on an infinite lattice of sites and are characterized by the locality and uniformity of their update rule. Permutations of the state set and isometric…
Molecular electronics and other technologies whose components comprise individual molecules have been pursued for half a century because the molecular scale represents the limit of miniaturisation of objects whose structure is tuneable for…
In this paper we propose a research programme for getting structural characterisations for 2-dimensional languages generated by self-assembling tiles. This is part of a larger programme on getting a formal foundation of parallel,…
DNA nanotechnology allows for the realization of complex nanoarchitectures in which the spatial arrangements of different constituents and most functions can be enabled by DNA. When optically active components are integrated in such…
DNA strand displacement systems have proven themselves to be fertile substrates for the design of programmable molecular machinery and circuitry. Domain-level reaction enumerators provide the foundations for molecular programming languages…
Recent advancements in microbiology have motivated the study of the production of nanostructures with applications such as biomedical computing and molecular robotics. One way to construct these structures is to construct branched DNA…
As a mathematical model of self-assembling systems, Winfree's abstract Tile Assembly Model (aTAM) is a remarkable platform for studying the behaviors and powers of self-assembling systems. Capable of Turing universal computation, the aTAM…