Boolean Functions Over Nano-Fabrics: Improving Resilience Through Coding

This paper determines mechanisms to mitigate errors when implementing Boolean functions in nano-circuits. Nano-fabrics are expected to have high defect rates as atomic variations directly impact such materials. This paper develops a coding mechanism that uses a combination of cheap, but unreliable nano-device as the main function and reliable, but expensive CMOS devices to implement the coding mechanism. The unique feature of this paper is that it exploits the don´t-cares that naturally occur in Boolean functions to construct better codes. The reliable Boolean function problem is cast as a constraint satisfaction problem and then solved using a tree-based dynamic programming algorithm. (Here, the word “dynamic programming” is used in the same sense as computer-science literature, i.e., and as an efficient search algorithm over trees).