Related papers: Verification in Staged Tile Self-Assembly

It is well-known that the question of whether a given finite region can be tiled with a given set of tiles is NP-complete. We show that the same is true for the right tromino and square tetromino on the square lattice, or for the right…

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…

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…

We characterize the complexity of the PATS problem for patterns of fixed height and color count in variants of the model where seed glues are either chosen or fixed and identical (so-called non-uniform and uniform variants). We prove that…

In this work we propose a generalization of Winfree's abstract Tile Assembly Model (aTAM) in which tile types are assigned rigid shapes, or geometries, along each tile face. We examine the number of distinct tile types needed to assemble…

In this thesis a comprehensive verification framework is proposed to contend with some important issues in composability verification and a verification process is suggested to verify composability of different kinds of systems models, such…

This short survey of recent work in tile self-assembly discusses the use of simulation to classify and separate the computational and expressive power of self-assembly models. The journey begins with the result that there is a single…

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…

We introduce a new property of tile self-assembly systems that we call size-separability. A system is size-separable if every terminal assembly is a constant factor larger than any intermediate assembly. Size-separability is motivated by…

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…

In pursuit of a deeper understanding of Boolean Promise Constraint Satisfaction Problems (PCSPs), we identify a class of problems with restricted structural complexity, which could serve as a promising candidate for complete…

We analyze the computational complexity of several new variants of edge-matching puzzles. First we analyze inequality (instead of equality) constraints between adjacent tiles, proving the problem NP-complete for strict inequalities but…

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…

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…

We prove that path puzzles with complete row and column information--or equivalently, 2D orthogonal discrete tomography with Hamiltonicity constraint--are strongly NP-complete, ASP-complete, and #P-complete. Along the way, we newly…

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,…

We introduce a 2-round stochastic constraint-satisfaction problem, and show that its approximation version is complete for (the promise version of) the complexity class AM. This gives a `PCP characterization' of AM analogous to the PCP…

Self-assembly in the laboratory can now yield `information-rich' nanostructures in which each component is of a distinct type and has a defined spatial position. Ensuring the thermodynamic stability of such structures requires…

Tile-based self-assembly systems are capable of universal computation and algorithmically-directed growth. Systems capable of such behavior typically make use of "glue cooperation" in which the glues on at least $2$ sides of a tile must…

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…