相关论文: Complexity of Self-Assembled Shapes
In 2004, Klavins et al. introduced the use of graph grammars to describe -- and to program -- systems of self-assembly. We show that these graph grammars can be embedded in a graph rewriting characterization of distributed systems that was…
Both biological and artificial self-assembly processes can take place by a range of different schemes, from the successive addition of identical building blocks, to hierarchical sequences of intermediates, all the way to the fully…
Patterned self-assembly is a process whereby coloured tiles self-assemble to build a rectangular coloured pattern. We propose self-assembly (SA) hypergraph automata as an automata-theoretic model for patterned self-assembly. We investigate…
Many forms of programmable matter have been proposed for various tasks. We use an abstract model of self-organizing particle systems for programmable matter which could be used for a variety of applications, including smart paint and…
Complexity theory can be viewed as the study of the relationship between computation and applications, understood the former as complexity classes and the latter as problems. Completeness results are clearly central to that view. Many…
Perhaps the two most significant theoretical questions about the programming of self-assembling agents are: (1) necessary and sufficient conditions to produce a unique terminal assembly, and (2) error correction. We address both questions,…
The Tile Assembly Model is a Turing universal model that Winfree introduced in order to study the nanoscale self-assembly of complex (typically aperiodic) DNA crystals. Winfree exhibited a self-assembly that tiles the first quadrant of the…
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,…
In resolving instances of a computational problem, if multiple instances of interest share a feature in common, it may be fruitful to compile this feature into a format that allows for more efficient resolution, even if the compilation is…
Models of computations over the integers are equivalent from a computability and complexity theory point of view by the Church-Turing thesis. It is not possible to unify discrete-time models over the reals. The situation is unclear but…
Algorithmic self-assembly occurs when disorganized components autonomously combine to form structures and, by their design and the dynamics of the system, are forced to follow the execution of algorithms. Motivated by applications in…
Self-assembly in natural and synthetic molecular systems can create complex aggregates or materials whose properties and functionality rises from their internal structure and molecular arrangement. The key microscopic features that control…
Spontaneous self-assembly in molecular systems is a fundamental route to both biological and engineered soft matter. Simple micellisation, emulsion formation, and polymer mixing principles are well understood. However, the principles behind…
Experiments have reached a monumental capacity for designing and synthesizing microscopic particles for self-assembly, making it possible to precisely control particle concentrations, shapes, and interactions. However, more physical insight…
In this paper, we present a theoretical effort to connect the theory of program size to psychology by implementing a concrete language of thought with Turing-computable Kolmogorov complexity (LT^2C^2) satisfying the following requirements:…
Geometric frustration offers a pathway to soft matter self-assembly with controllable finite sizes. While the understanding of frustration in soft matter assembly derives almost exclusively from continuum elastic descriptions, a current…
Many remarkably robust, rapid and spontaneous self-assembly phenomena in nature can be modeled geometrically starting from a collection of rigid bunches of spheres. This paper highlights the role of symmetry in sphere-based assembly…
Type systems as a way to control or analyze programs have been largely studied in the context of functional programming languages. Some of those work allow to extract from a typing derivation for a program a complexity bound on this…
Since its introduction by Erik Winfree in 1998, the abstract Tile Assembly Model (aTAM) has inspired a wealth of research. As an abstract model for tile based self-assembly, it has proven to be remarkably powerful and expressive in terms of…
Kinematics of mechanisms is intricately coupled to their geometry and their utility often arises out of the ability to perform reproducible motion with fewer actuating degrees of freedom. In this article, we explore the assembly of…