Formal methods for the analysis and synthesis of nanometer-scale cellular arrays

Abstract

Nanometer-scale structures suitable for computing have been investigated by several research groups in recent years. A common feature of these structures is their dynamic evolution through cascaded local interactions embedded on a discrete grid. Finding configurations capable of conducting computations is a task that often requires tedious experiments in laboratories. Formal methods—though used extensively for the specification and verification of software and hardware computing systems—are virtually unexplored with respect to computational structures at atomic scales. This paper presents a systematic approach toward the application of formal methods in this context, using techniques like abstraction, model-checking, and symbolic representations of states to explore and discover computational structures. The proposed techniques are applied to a system of CO molecules on a grid of Copper atoms, resulting in the design of a complete library of combinational logic gates based on this molecular system. The techniques are also applied on (more general) systems of cellular automata that employ an asynchronous mode of timing. The use of formal methods may narrow the gap between Physical Chemistry and Computer Science, allowing the description of interactions of nanometer scale systems on a level of abstraction suitable to devise computing devices.