We know that tilesets that can tile the plane always admit a quasiperiodic tiling [4, 8], yet they hold many uncomputable properties [3, 11, 21, 25]. The quasi-periodicity function is one way to measure the regularity of a quasiperiodic tiling. We prove that the tilings by a tileset that admits only quasiperiodic tilings have a recursively (and uniformly) bounded quasi-periodicity function. Thi...

While algorithmic DNA self-assembly is, in theory, capable of forming complex patterns, its experimental demonstration has been limited by significant assembly errors. In this paper we describe a novel protection/deprotection strategy to strictly enforce the direction of tiling assembly growth to ensure the robustness of the assembly process. Tiles are initially inactive, meaning that each tile...

Article history: Received 28 January 2014 Accepted 6 June 2014 Available online 23 June 2014 Communicated by D.-Z. Du

Dominoes is a popular and well-known game possibly dating back three millennia. Players are given a set of domino tiles, each with two labeled square faces, and take turns connecting them into a growing chain of dominoes by matching identical faces. We show that singleplayer dominoes is in P, while multiplayer dominoes is hard: when players cooperate, the game is NP-complete, and when players c...

We study some decision problems concerning the tiling of the plane with Wang tiles We present a proof for the undecidability of the tiling problem for the whole plane and also for the periodic tiling In these poofs an aperiodic tile set is constructed We are interested in the second part in the link between the cardinality of possible tilings of the plane with a given tile set and the existence...

In this thesis we study self-assembly systems, in particular, we focus on the tile complexity of shapes. Using the standard tile assembly model proposed by Rothemund and Winfree, we give two lower bounds on the tile complexity of arbitrary shapes in terms of the radius and diameter of the shape. Applying our results to a square yields a partial answer to a problem of Rothemund and Winfree. We a...

The identification of technologically innovating firms is related to the development of indicators of their innovation activity. In this study, we carry out a review of indicators of firms’ technological innovation activity and then classify them according to whether they are based on inputs or outputs of the innovation process, and to the sources of the information they consider, whether prima...

Tiling is widely used by compilers and programmer to optimize scientific and engineering code for better performance. Many parallel programming languages support tile/tiling directly through first-class language constructs or library routines. However, the current OpenMP programming language is tile oblivious, although it is the de facto standard for writing parallel programs on shared memory s...