47 research outputs found
Combinatorial optimization problems in self-assembly
Self-assembly is the ubiquitous process by which simple objects autonomously assemble into intricate complexes. It has been suggested that intricate self-assembly processes will ultimately be used in circuit fabrication, nano-robotics, DNA computation, and amorphous computing. In this paper, we study two combinatorial optimization problems related to efficient self-assembly of shapes in the Tile Assembly Model of self-assembly proposed by Rothemund and Winfree [18]. The first is the Minimum Tile Set Problem, where the goal is to find the smallest tile system that uniquely produces a given shape. The second is the Tile Concentrations Problem, where the goal is to decide on the relative concentrations of different types of tiles so that a tile system assembles as quickly as possible. The first problem is akin to finding optimum program size, and the second to finding optimum running time for a "program" to assemble the shape.Self-assembly is the ubiquitous process by which simple objects autonomously assemble into intricate complexes. It has been suggested that intricate self-assembly processes will ultimately be used in circuit fabrication, nano-robotics, DNA computation, and amorphous computing. In this paper, we study two combinatorial optimization problems related to efficient self-assembly of shapes in the Tile Assembly Model of self-assembly proposed by Rothemund and Winfree [18]. The first is the Minimum Tile Set Problem, where the goal is to find the smallest tile system that uniquely produces a given shape. The second is the Tile Concentrations Problem, where the goal is to decide on the relative concentrations of different types of tiles so that a tile system assembles as quickly as possible. The first problem is akin to finding optimum program size, and the second to finding optimum running time for a "program" to assemble the shape. We prove that the first problem is NP-complete in general, and polynomial time solvable on trees and squares. In order to prove that the problem is in NP, we present a polynomial time algorithm to verify whether a given tile system uniquely produces a given shape. This algorithm is analogous to a program verifier for traditional computational systems, and may well be of independent interest. For the second problem, we present a polynomial time -approximation algorithm that works for a large class of tile systems that we call partial order systems
Finding irreducible polynomials over finite fields
Wetensch. publicatieFaculteit der Wiskunde en Natuurwetenschappe
On Applying Molecular Computation to the Data Encryption Standard
Recently, Boneh, Dunworth, and Lipton (1996) described the potential use of molecular computation in attacking the United States Data
Encryption Standard (DES), Here, we provide a description of such an
attack using the sticker model of molecular computation. Our analysis
suggests that such an attack might be mounted on a tabletop machine
using approximately a gram of DNA and might succeed even in the
presence of a large number of errors
On Constructing A Molecular Computer
It has recently been suggested that under some circumstances computers based on molecular interactions may be a viable alternative to computers based on electronics. Here, some practical aspects of constructing a molecular computer are considered. 1 Introduction In [Ad] a small instance of the so called `Hamiltonian path problem' was encoded in molecules of DNA and solved in a test tube using standard methods of molecular biology. It was asserted that for certain problems, molecular computers might compete with electronic computers. At the time that [Ad] appeared, there seemed to be formidable obstructions to creating a practical molecular computer. Roughly, these obstructions were of two types: ffl Physical obstructions arising primarily from difficulties in dealing with large scale systems and in coping with errors. ffl Logical obstructions concerning the versatility of molecular computers and their capacity to efficiently accommodate a wide variety of computational problems. R..
Molecular Computation Of Solutions To Combinatorial Problems
The tools of molecular biology are used to solve an instance of the directed Hamiltonian path problem. A small graph is encoded in molecules of DNA and the `operations' of the computation are performed with standard protocols and enzymes. This experiment demonstrates the feasibility of carrying out computations at the molecular level