Related papers: Unique Assembly Verification in Two-Handed Self-As…

This paper introduces the theory and practice of formal verification of self-assembling systems. We interpret a well-studied abstraction of nanomolecular self assembly, the Abstract Tile Assembly Model (aTAM), into Computation Tree Logic…

In this paper, we prove that in the abstract Tile Assembly Model (aTAM), an accretion-based model which only allows for a single tile to attach to a growing assembly at each step, there are no tile assembly systems capable of…

In this paper we consider the problem of the strict self-assembly of infinite fractals within tile self-assembly. In particular, we provide tile assembly algorithms for the assembly of the discrete Sierpinski triangle and the discrete…

Self-assembly is a process which is ubiquitous in natural, especially biological systems. It occurs when groups of relatively simple components spontaneously combine to form more complex structures. While such systems have inspired a large…

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…

We introduce a new model of algorithmic tile self-assembly called size-dependent assembly. In previous models, supertiles are stable when the total strength of the bonds between any two halves exceeds some constant temperature. In this…

We show that the Tile Assembly Model exhibits a strong notion of universality where the goal is to give a single tile assembly system that simulates the behavior of any other tile assembly system. We give a tile assembly system that is…

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…

Is Winfree's abstract Tile Assembly Model (aTAM) "powerful?" Well, if certain tiles are required to "cooperate" in order to be able to bind to a growing tile assembly (a.k.a., temperature 2 self-assembly), then Turing universal computation…

We prove that the abstract Tile Assembly Model (aTAM) of nanoscale self-assembly is intrinsically universal. This means that there is a single tile assembly system U that, with proper initialization, simulates any tile assembly system T.…

We consider non-cooperative binding, so-called 'temperature 1', in deterministic or directed (called here confluent) tile self-assembly systems in two dimensions and show a necessary and sufficient condition for such system to have an…

We prove a Pumping Lemma for the noncooperative abstract Tile Assembly Model, a model central to the theory of algorithmic self-assembly since the beginning of the field. This theory suggests, and our result proves, that small differences…

Traditionally, computation within self-assembly models is hard to conceal because the self-assembly process generates a crystalline assembly whose computational history is inherently part of the structure itself. With no way to remove…

This paper concerns the self-assembly of scaled-up versions of arbitrary finite shapes. We work in the multiple temperature model that was introduced by Aggarwal, Cheng, Goldwasser, Kao, and Schweller (Complexities for Generalized Models of…

We define the Reflexive Tile Assembly Model (RTAM), which is obtained from the abstract Tile Assembly Model (aTAM) by allowing tiles to reflect across their horizontal and/or vertical axes. We show that the class of directed temperature-1…

In this paper we demonstrate the power of a model of tile self-assembly based on active glues which can dynamically change state. We formulate the Signal-passing Tile Assembly Model (STAM), based on the model of Padilla, Liu, and Seeman to…

We consider the tile self-assembly model and how tile complexity can be eliminated by permitting the temperature of the self-assembly system to be adjusted throughout the assembly process. To do this, we propose novel techniques for…

Unmanned aerial vehicles (UAVs) have been used for many applications in recent years, from urban search and rescue, to agricultural surveying, to autonomous underground mine exploration. However, deploying UAVs in tight, indoor spaces,…

We prove the computational weakness of a model of tile assembly that has so far resisted many attempts of formal analysis or positive constructions. Specifically, we prove that, in Winfree's abstract Tile Assembly Model, when restricted to…

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,…