The dominating set problem is a well known NP hard problem. It means that as the instance size grows, they quickly become impossible to solve on traditional digital computers. Tile assembly model has been demonstrated as a highly distributed parallel model of computation. Algorithmic tile assembly has been proved to be Turing-universal. This paper proposes a tile assembly system for the dominat...

This report was written by Dr. Donald Fraser of the Department of Paediatrics, Universit!/ of Toronto and The Hospital for Sick Children, Toronto, Ontario, Canada, in consultation with tile Conirnittee Ofl Nutrition of the American Academy of Pediatrics. The /)OSltiOhb taken on the issue examined reflects the current opinion of tile Committee and i)rovi(les tile .ccie iti/ic background for the ...

Power-aware graphics architectures are receiving more attention recently. In this paper we analyze rendering techniques suitable for low power devices. One technique that looks promising is Tile Rendering. This technique decomposes a scene into tiles and renders each tile independently. For several scenes we compute a tile size that allows most triangles to be rendered without being divided int...

We prove that if a set X ⊆ Z2 weakly self-assembles at temperature 1 in a deterministic (Winfree) tile assembly system satisfying a natural condition known as pumpability, then X is a finite union of semi-doubly periodic sets. This shows that only the most simple of infinite shapes and patterns can be constructed using pumpable temperature 1 tile assembly systems, and gives evidence for the the...

We present an technique for developing a single, aperiodic (or universal) tile that does not overlap. We provide two examples, constructed by converting overlapping regions of Gummelt’s decagon cover to interleaved regions in a porous tile. Each is a bounded, dense, sponge-like set of points in 2 that tiles the plane aperiodically. One tile has measure zero, the other has positive measure every...

Algorithmic self-assembly, a generalization of crystal growth, has been proposed as a mechanism for bottom-up fabrication of complex nanostructures and autonomous DNA computation. In principle, growth can be programmed by designing a set of molecular tiles with binding interactions that enforce assembly rules. In practice, however, errors during assembly cause undesired products, drastically re...

A subset V ⊆ Fn2 is a tile if F n 2 can be covered by disjoint translates of V . In other words, V is a tile if and only if there is a subset A ⊆ Fn2 such that V + A = Fn2 uniquely (i.e., v + a = v ′ + a′ implies that v = v′ and a = a′ where v, v′ ∈ V and a, a′ ∈ A). In some problems in coding theory and hashing we are given a putative tile V , and wish to know whether or not it is a tile. In t...

Self-assembly is a fundamental process by which supramolecular species form spontaneously from their components. This process is ubiquitous throughout the life chemistry and is central to biological information processing. Algorithms for solving many mathematical and computational problems via tile self assembly has been proposed by many researchers in the last decade. In particular tile set fo...

In this paper, we introduce a novel approach to guide tile size selection by employing analytical models to limit empirical search within a subspace of the full search space. Two analytical models are used together: 1) an existing conservative model, based on the data footprint of a tile, which ignores intra-tile cache block replacement, and 2) an aggressive new model that assumes optimal cache...

Tile logic extends rewriting logic by taking into account side-eeects and rewriting synchronization. These aspects are very important when we model process calculi, because they allow us to express the dynamic interaction between processes and \the rest of the world". Since rewriting logic is the semantic basis of several language implementation eeorts, an executable speciication of tile system...