Concentration independent random number generation in tile self-assembly
نویسندگان
چکیده
منابع مشابه
Concentration independent random number generation in tile self-assembly
In this paper we introduce the robust coin flip problem in which one must design an abstract tile assembly system (aTAM system) whose terminal assemblies can be partitioned such that the final assembly lies within either partition with exactly probability 1/2, regardless of what relative concentration assignment is given to the tile types of the system. We show that robust coin flipping is poss...
متن کاملFlipping Tiles: Concentration Independent Coin Flips in Tile Self-Assembly
In this paper we introduce the robust coin flip problem in which one must design an abstract tile assembly system (aTAM system) whose terminal assemblies can be partitioned such that the final assembly lies within either partition with exactly probability 1/2, regardless of what relative concentration assignment is given to the tile types of the system. We show that robust coin flipping is poss...
متن کاملRandom Number Selection in Self-assembly
We investigate methods for exploiting nondeterminism inherent within the Tile Assembly Model in order to generate uniform random numbers. Namely, given an integer range {0, . . . , n− 1}, we exhibit methods for randomly selecting a number within that range. We present three constructions exhibiting a trade-off between space requirements and closeness to uniformity. The first selector selects a ...
متن کاملVerification in Staged Tile Self-Assembly
We prove the unique assembly and unique shape verification problems, benchmark measures of self-assembly model power, are coNP-hard and contained in PSPACE (and in Πp2s for staged systems with s stages). En route, we prove that unique shape verification problem in the 2HAM is coNP-complete.
متن کاملTriangular and Hexagonal Tile Self-Assembly Systems Triangular and Hexagonal Tile Self-Assembly Systems
We discuss theoretical aspects of the self-assembly of triangular tiles, in particular, right triangular tiles and equilateral triangular tiles, and the self-assembly of hexagonal tiles. Contrary to intuition, we show that triangular tile assembly systems and square tile assembly systems cannot be simulated by each other in a non-trivial way. More precisely, there exists a square tile assembly ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2017
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2016.12.021