A space-efficient randomized DNA algorithm for k-SAT

Abstract

We present a randomized DNA algorithm for k-SAT based on the classical algorithm of Paturi et al. [8]. For an n-variable, m-clause instance of k-SAT (m > n), our algorithm finds a satisfying assignment, assuming one exists, with probability 1−e ^−α, in worst-case time O(k ² mn) and space O(2^{(1−1/k)n+logα}). This makes it the most space-efficient DNA k-SAT algorithm for k > 3 and k < n/log α (i.e. the clause size is small compared to the number of variables). In addition, our algorithm is the first DNA algorithm to adapt techniques from the field of randomized classical algorithms.

This work was done while at the Department of Computer Science, Princeton University, Princeton, NJ 08544, USA.

This work was done while at the Department of Mathematics, Princeton University, Princeton, NJ 08544, USA.