Random Number Selection in Self-assembly

Abstract. 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 random number with probability Θ(1/n) using O(log2 n) tiles. The second selector takes a user-specified parameter that guarantees the probabilities are arbitrarily close to uniform, at the cost of additional space. The third selector selects a random number with probability exactly 1/n, and uses no more space than the first selector with high probability, but uses potentially unbounded space.

• Type: Conference
• Year: 2009
• Where: UC
• Authors: David Doty, Jack H. Lutz, Matthew J. Patitz, Scott M. Summers, Damien Woods
• Keywords: Applied Computing, Random Number, UC 2009, Uniform Random Numbers, first Selector