8,893 research outputs found
Optimal Staged Self-Assembly of General Shapes
We analyze the number of tile types , bins , and stages necessary to
assemble squares and scaled shapes in the staged tile assembly
model. For squares, we prove stages suffice and
are necessary for almost all .
For shapes with Kolmogorov complexity , we prove
stages suffice and are necessary to
assemble a scaled version of , for almost all . We obtain similarly tight
bounds when the more powerful flexible glues are permitted.Comment: Abstract version appeared in ESA 201
Design of Geometric Molecular Bonds
An example of a nonspecific molecular bond is the affinity of any positive
charge for any negative charge (like-unlike), or of nonpolar material for
itself when in aqueous solution (like-like). This contrasts specific bonds such
as the affinity of the DNA base A for T, but not for C, G, or another A. Recent
experimental breakthroughs in DNA nanotechnology demonstrate that a particular
nonspecific like-like bond ("blunt-end DNA stacking" that occurs between the
ends of any pair of DNA double-helices) can be used to create specific
"macrobonds" by careful geometric arrangement of many nonspecific blunt ends,
motivating the need for sets of macrobonds that are orthogonal: two macrobonds
not intended to bind should have relatively low binding strength, even when
misaligned.
To address this need, we introduce geometric orthogonal codes that abstractly
model the engineered DNA macrobonds as two-dimensional binary codewords. While
motivated by completely different applications, geometric orthogonal codes
share similar features to the optical orthogonal codes studied by Chung,
Salehi, and Wei. The main technical difference is the importance of 2D geometry
in defining codeword orthogonality.Comment: Accepted to appear in IEEE Transactions on Molecular, Biological, and
Multi-Scale Communication
Particle Computation: Complexity, Algorithms, and Logic
We investigate algorithmic control of a large swarm of mobile particles (such
as robots, sensors, or building material) that move in a 2D workspace using a
global input signal (such as gravity or a magnetic field). We show that a maze
of obstacles to the environment can be used to create complex systems. We
provide a wide range of results for a wide range of questions. These can be
subdivided into external algorithmic problems, in which particle configurations
serve as input for computations that are performed elsewhere, and internal
logic problems, in which the particle configurations themselves are used for
carrying out computations. For external algorithms, we give both negative and
positive results. If we are given a set of stationary obstacles, we prove that
it is NP-hard to decide whether a given initial configuration of unit-sized
particles can be transformed into a desired target configuration. Moreover, we
show that finding a control sequence of minimum length is PSPACE-complete. We
also work on the inverse problem, providing constructive algorithms to design
workspaces that efficiently implement arbitrary permutations between different
configurations. For internal logic, we investigate how arbitrary computations
can be implemented. We demonstrate how to encode dual-rail logic to build a
universal logic gate that concurrently evaluates and, nand, nor, and or
operations. Using many of these gates and appropriate interconnects, we can
evaluate any logical expression. However, we establish that simulating the full
range of complex interactions present in arbitrary digital circuits encounters
a fundamental difficulty: a fan-out gate cannot be generated. We resolve this
missing component with the help of 2x1 particles, which can create fan-out
gates that produce multiple copies of the inputs. Using these gates we provide
rules for replicating arbitrary digital circuits.Comment: 27 pages, 19 figures, full version that combines three previous
conference article
Nonterrestrial utilization of materials: Automated space manufacturing facility
Four areas related to the nonterrestrial use of materials are included: (1) material resources needed for feedstock in an orbital manufacturing facility, (2) required initial components of a nonterrestrial manufacturing facility, (3) growth and productive capability of such a facility, and (4) automation and robotics requirements of the facility
Randomness, information encoding, and shape replication in various models of DNA-inspired self-assembly
Self-assembly is the process by which simple, unorganized components autonomously combine to form larger, more complex structures. Researchers are turning to self-assembly technology for the design of ever smaller, more complex, and precise nanoscale devices, and as an emerging fundamental tool for nanotechnology.
We introduce the robust random number generation problem, the problem of encoding a target string of bits in the form of a bit string pad, and the problem of shape replication in various models of tile-based self-assembly. Also included are preliminary results in each of these directions with discussion of possible future work directions
Freezing, Bounded-Change and Convergent Cellular Automata *
This paper studies three classes of cellular automata from a computational point of view: freezing cellular automata where the state of a cell can only decrease according to some order on states, cellular automata where each cell only makes a bounded number of state changes in any orbit, and finally cellular automata where each orbit converges to some fixed point. Many examples studied in the literature fit into these definitions, in particular the works on cristal growth started by S. Ulam in the 60s. The central question addressed here is how the computational power and computational hardness of basic properties is affected by the constraints of convergence, bounded number of change, or local decreasing of states in each cell. By studying various benchmark problems (short-term prediction, long term reachability, limits) and considering various complexity measures and scales (LOGSPACE vs. PTIME, communication complexity, Turing computability and arithmetical hierarchy) we give a rich and nuanced answer: the overall computational complexity of such cellular automata depends on the class considered (among the three above), the dimension , and the precise problem studied. In particular, we show that all settings can achieve universality in the sense of Blondel-Delvenne-Kurka, although short term predictability varies from NLOGSPACE to P-complete. Besides, the computability of limit configurations starting from computable initial configurations separates bounded-change from convergent cellular automata in dimension 1, but also dimension 1 versus higher dimensions for freezing cellular automata. Another surprising dimension-sensitive result obtained is that nilpotency becomes decidable in dimension 1 for all the three classes, while it stays undecidable even for freezing cellular automata in higher dimension
Freezing, Bounded-Change and Convergent Cellular Automata *
This paper studies three classes of cellular automata from a computational point of view: freezing cellular automata where the state of a cell can only decrease according to some order on states, cellular automata where each cell only makes a bounded number of state changes in any orbit, and finally cellular automata where each orbit converges to some fixed point. Many examples studied in the literature fit into these definitions, in particular the works on cristal growth started by S. Ulam in the 60s. The central question addressed here is how the computational power and computational hardness of basic properties is affected by the constraints of convergence, bounded number of change, or local decreasing of states in each cell. By studying various benchmark problems (short-term prediction, long term reachability, limits) and considering various complexity measures and scales (LOGSPACE vs. PTIME, communication complexity, Turing computability and arithmetical hierarchy) we give a rich and nuanced answer: the overall computational complexity of such cellular automata depends on the class considered (among the three above), the dimension , and the precise problem studied. In particular, we show that all settings can achieve universality in the sense of Blondel-Delvenne-Kurka, although short term predictability varies from NLOGSPACE to P-complete. Besides, the computability of limit configurations starting from computable initial configurations separates bounded-change from convergent cellular automata in dimension 1, but also dimension 1 versus higher dimensions for freezing cellular automata. Another surprising dimension-sensitive result obtained is that nilpotency becomes decidable in dimension 1 for all the three classes, while it stays undecidable even for freezing cellular automata in higher dimension
Line-Recovery by Programmable Particles
Shape formation has been recently studied in distributed systems of
programmable particles. In this paper we consider the shape recovery problem of
restoring the shape when of the particles have crashed. We focus on the
basic line shape, used as a tool for the construction of more complex
configurations.
We present a solution to the line recovery problem by the non-faulty
anonymous particles; the solution works regardless of the initial distribution
and number of faults, of the local orientations of the non-faulty
entities, and of the number of non-faulty entities activated in each round
(i.e., semi-synchronous adversarial scheduler)
- …