11 research outputs found
Towards the Design of Heuristics by Means of Self-Assembly
The current investigations on hyper-heuristics design have sprung up in two
different flavours: heuristics that choose heuristics and heuristics that
generate heuristics. In the latter, the goal is to develop a problem-domain
independent strategy to automatically generate a good performing heuristic for
the problem at hand. This can be done, for example, by automatically selecting
and combining different low-level heuristics into a problem specific and
effective strategy. Hyper-heuristics raise the level of generality on automated
problem solving by attempting to select and/or generate tailored heuristics for
the problem at hand. Some approaches like genetic programming have been
proposed for this. In this paper, we explore an elegant nature-inspired
alternative based on self-assembly construction processes, in which structures
emerge out of local interactions between autonomous components. This idea
arises from previous works in which computational models of self-assembly were
subject to evolutionary design in order to perform the automatic construction
of user-defined structures. Then, the aim of this paper is to present a novel
methodology for the automated design of heuristics by means of self-assembly
Temperature 1 Self-Assembly: Deterministic Assembly in 3D and Probabilistic Assembly in 2D
We investigate the power of the Wang tile self-assembly model at temperature
1, a threshold value that permits attachment between any two tiles that share
even a single bond. When restricted to deterministic assembly in the plane, no
temperature 1 assembly system has been shown to build a shape with a tile
complexity smaller than the diameter of the shape. In contrast, we show that
temperature 1 self-assembly in 3 dimensions, even when growth is restricted to
at most 1 step into the third dimension, is capable of simulating a large class
of temperature 2 systems, in turn permitting the simulation of arbitrary Turing
machines and the assembly of squares in near optimal
tile complexity. Further, we consider temperature 1 probabilistic assembly in
2D, and show that with a logarithmic scale up of tile complexity and shape
scale, the same general class of temperature systems can be simulated
with high probability, yielding Turing machine simulation and
assembly of squares with high probability. Our results show a sharp
contrast in achievable tile complexity at temperature 1 if either growth into
the third dimension or a small probability of error are permitted. Motivated by
applications in nanotechnology and molecular computing, and the plausibility of
implementing 3 dimensional self-assembly systems, our techniques may provide
the needed power of temperature 2 systems, while at the same time avoiding the
experimental challenges faced by those systems
Proceedings of JAC 2010. JournĂŠes Automates Cellulaires
The second Symposium on Cellular Automata âJourn´ees Automates Cellulairesâ (JAC 2010) took place in Turku, Finland, on December 15-17, 2010. The first two conference days were held in the Educarium building of the University of Turku, while the talks of the third day were given onboard passenger ferry boats in the beautiful Turku archipelago, along the route TurkuâMariehamnâTurku. The conference was organized by FUNDIM, the Fundamentals of Computing and Discrete Mathematics research center at the mathematics department of the University of Turku.
The program of the conference included 17 submitted papers that were selected by the international program committee, based on three peer reviews of each paper. These papers form the core of these proceedings. I want to thank the members of the program committee and the external referees for the excellent work that have done in choosing the papers to be presented in the conference. In addition to the submitted papers, the program of JAC 2010 included four distinguished invited speakers: Michel Coornaert (Universit´e de Strasbourg, France), Bruno Durand (Universit´e de Provence, Marseille, France), Dora Giammarresi (Universit` a di Roma Tor Vergata, Italy) and Martin Kutrib (Universit¨at Gie_en, Germany). I sincerely thank the invited speakers for accepting our invitation to come and give a plenary talk in the conference. The invited talk by Bruno Durand was eventually given by his co-author Alexander Shen, and I thank him for accepting to make the presentation with a short notice. Abstracts or extended abstracts of the invited presentations appear in the first part of this volume.
The program also included several informal presentations describing very recent developments and ongoing research projects. I wish to thank all the speakers for their contribution to the success of the symposium. I also would like to thank the sponsors and our collaborators: the Finnish Academy of Science and Letters, the French National Research Agency project EMC (ANR-09-BLAN-0164), Turku Centre for Computer Science, the University of Turku, and Centro Hotel. Finally, I sincerely thank the members of the local organizing committee for making the conference possible.
These proceedings are published both in an electronic format and in print. The electronic proceedings are available on the electronic repository HAL, managed by several French research agencies. The printed version is published in the general publications series of TUCS, Turku Centre for Computer Science. We thank both HAL and TUCS for accepting to publish the proceedings.Siirretty Doriast
Hamiltonian Complexity in Many-Body Quantum Physics
The development of quantum computers has promised to greatly improve our understanding of quantum many-body physics.
However, many physical systems display complex and unpredictable behaviour which is not amenable to analytic or even computational solutions.
This thesis aims to further our understanding of what properties of physical systems a quantum computer is capable of determining, and simultaneously explore the behaviour of exotic quantum many-body systems.
First, we analyse the task of determining the phase diagram of a quantum material, and thereby charting its properties as a function of some externally controlled parameter.
In the general case we find that determining the phase diagram to be uncomputable, and in special cases show it is P^{QMA_{EXP}}-complete.
Beyond this, we examine how a common method for determining quantum phase transitions --- the Renormalisation Group (RG) --- fails when applied to a set of Hamiltonians with uncomputable properties.
We show that for such Hamiltonians (a) there is a well-defined RG procedure, but this procedure must fail to predict the uncomputable properties (b) this failure of the RG procedure demonstrates previously unseen and novel behaviour.
We also formalise in terms of a promise problem, the question of computing the ground state energy per particle of a model in the limit of an infinitely large system, and show that approximating this quantity is likely intractable.
In doing this we develop a new kind of complexity question concerned with determining the precision to which a single number can be determined.
Finally we consider the problem of measuring local observables in the low energy subspace of systems --- an important problem for experimentalists and theorists alike.
We prove that if a certain kind of construction exists for a class of Hamiltonians, , the results about hardness of determining the ground state energy directly implies hardness results for measuring observables at low energies
Algorithmic Assembly of Nanoscale Structures
The development of nanotechnology has become one of the most significant endeavors of our time. A natural objective of this field is discovering how to engineer nanoscale structures. Limitations of current top-down techniques inspire investigation into bottom-up approaches to reach this objective. A fundamental precondition for a bottom-up approach is the ability to control the behavior of nanoscale particles. Many abstract representations have been developed to model systems of particles and to research methods for controlling their behavior. This thesis develops theories on two such approaches for building complex structures: the self-assembly of simple particles, and the use of simple robot swarms. The concepts for these two approaches are straightforward. Self-assembly is the process by which simple particles, following the rules of some behavior-governing system, naturally coalesce into a more complex form. The other method of bottom-up assembly involves controlling nanoscale particles through explicit directions and assembling them into a desired form. Regarding the self-assembly of nanoscale structures, we present two construction methods in a variant of a popular theoretical model known as the 2-Handed Tile Self-Assembly Model. The first technique achieves shape construction at only a constant scale factor, while the second result uses only a constant number of unique particle types. Regarding the use of robot swarms for construction, we first develop a novel technique for reconfiguring a swarm of globally-controlled robots into a desired shape even when the robots can only move maximally in a commanded direction. We then expand on this work by formally defining an entire hierarchy of shapes which can be built in this manner and we provide a technique for doing so
Self-Assembly of Tiles: Theoretical Models, the Power of Signals, and Local Computing
DNA-based self-assembly is an autonomous process whereby a disordered system of DNA sequences forms an organized structure or pattern as a consequence of Watson-Crick complementarity of DNA sequences, without external direction.
Here, we propose self-assembly (SA) hypergraph automata as an automata-theoretic model for patterned self-assembly. We investigate the computational power of SA-hypergraph automata and show that for every recognizable picture language, there exists an SA-hypergraph automaton that accepts this language. Conversely, we prove that for any restricted SA-hypergraph automaton, there exists a Wang Tile System, a model for recognizable picture languages, that accepts the same language.
Moreover, we investigate the computational power of some variants of the Signal-passing Tile Assembly Model (STAM), as well as propose the concept of {\it Smart Tiles}, i.e., tiles with glues that can be activated or deactivated by signals, and which possess a limited amount of local computing capability. We demonstrate the potential of smart tiles to perform some robotic tasks such as replicating complex shapes