An aperiodic tile set is a finite set of tiles which can tile the plane (i.e. cover it without overlap), but not in a periodic way (i.e., no tiling is invariant by a translation). To prove the undecidability of the the Domino problem, Robert Berger constructed in 1966 the first aperiodic tile set [1]. His proof was simplified in 1971 by Rafael Robinson, who introduced a six-tile set and proved ...

. A very brief presentation of the physics prospects for the SLAC B-Factory, now under construction, is presented. Presented at tile ~Sth Interna,tionaJ Col~ferel)ce on High I;nergy l’ll)~sj(’s Warsaw, Polancl 25-31 <July 1996 “Work supported by the Department of’ Energy uncler contract [) E-~4C;ol;-76SFO0515. PHYSICS PROSPECTS FOR THE SLAC B-FACTORY

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...

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...