Related papers: Intrinsic Universality in Seeded Active Tile Self-…
Harnessing the intrinsic dynamics of physical systems for information processing opens new avenues for computation embodied in matter. Using simulations of a model system, we show that assemblies of DNA tiles capable of self-organizing into…
The fixed point construction is a method for designing tile sets and cellular automata with highly nontrivial dynamical and computational properties. It produces an infinite hierarchy of systems where each layer simulates the next one. The…
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…
This talk advocates intrinsic universality as a notion to identify simple cellular automata with complex computational behavior. After an historical introduction and proper definitions of intrinsic universality, which is discussed with…
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…
The paper proposes a simple formalism for dealing with deterministic, non-deterministic and stochastic cellular automata in a unifying and composable manner. Armed with this formalism, we extend the notion of intrinsic simulation between…
Universality in cellular automata theory is a central problem studied and developed from their origins by John von Neumann. In this paper, we present an algorithm where any Turing machine can be converted to one-dimensional cellular…
Cognitive computation such as e.g. language processing, is conventionally regarded as Turing computation, and Turing machines can be uniquely implemented as nonlinear dynamical systems using generalized shifts and subsequent G\"odel…
Tile assembly systems in the abstract Tile Assembly Model (aTAM) are computationally universal and capable of building complex shapes, but DNA-based implementations encounter formidable error rates that stifle this theoretical potential.…
In this paper we define the Dupled abstract Tile Assembly Model (DaTAM), which is a slight extension to the abstract Tile Assembly Model (aTAM) that allows for not only the standard square tiles, but also "duple" tiles which are rectangles…
In this paper, we introduce a sparse Tsetlin Machine (TM) with absorbing Tsetlin Automata (TA) states. In brief, the TA of each clause literal has both an absorbing Exclude- and an absorbing Include state, making the learning scheme…
The notions of universality and completeness are central in the theories of computation and computational complexity. However, proving lower bounds and necessary conditions remains hard in most of the cases. In this article, we introduce…
We consider non cooperative binding in so called `temperature 1', in deterministic (here called {\it confluent}) tile self-assembly systems (1-TAS) and prove the standing conjecture that such systems do not have universal computational…
A Cellular Automata (CA) rule is presented that can generate "loop patterns" in a 2D grid under fixed boundary conditions. A loop is a cyclically closed path represented by one-cells enclosed by zero-cells. A loop pattern can contain…
We present a suite of algorithmic techniques for handling substitution tilings by treating a tile's hierarchy of supertiles in a purely combinatorial fashion using finite state automata. The resulting techniques are very convenient for…
We ask the question of how small a self-assembling set of tiles can be yet have interesting computational behaviour. We study this question in a model where supporting walls are provided as an input structure for tiles to grow along: we…
In this paper we show that passive self-assembly in the context of the tile self-assembly model is capable of performing fuel efficient, universal computation. The tile self-assembly model is a premiere model of self-assembly in which…
We introduce staged self-assembly of Wang tiles, where tiles can be added dynamically in sequence and where intermediate constructions can be stored for later mixing. This model and its various constraints and performance measures are…
We show the first non-trivial positive algorithmic results (i.e. programs whose output is larger than their size), in a model of self-assembly that has so far resisted many attempts of formal analysis or programming: the planar…
Majumder, Reif and Sahu have presented a stochastic model of reversible, error-permitting, two-dimensional tile self-assembly, and showed that restricted classes of tile assembly systems achieved equilibrium in (expected) polynomial time.…