How can Programmable Logic Arrays (PLAs) be built without relying on lithography to pattern their smallest features? In this paper, we detail designs which exploit emerging, bottom-up material synthesis techniques to build PLAs using molecular-scale nanowires. Our new designs accommodate technologies where the only post-fabrication programmable element is a non-restoring diode. We introduce stochastic techniques which allow us to restore the diode logic at the nanoscale so that it can be cascaded and interconnected for general logic evaluation. Under conservative assumptions using 10nm nanowires and 90nm lithographic support, we project yielded logic density around 500,000nm^2/or term for a 60 or-term array; a complete 60-term, two-level...