Robustness and Games Against Nature in Molecular Programming

Abstract: Matter, especially DNA, is now programmed to carry out useful processes at the nanoscale. As these programs and processes become more complex and their envisioned safety-critical applications approach deployment, it is essential to develop methods for engineering trustworthiness into molecular programs. Some of this can be achieved by adapting existing software engineering methods, but molecular programming also presents new challenges that will require new methods. This paper presents a method for dealing with one such challenge, namely, the difficulty of ascertaining how robust a molecular program is to perturbations of the relative "clock speeds" of its various reactions. The method proposed here is game-theoretic. The robustness of a molecular program is quantified in terms of its ability to win (achieve its original objective) in games against other molecular programs that manipulate its relative clock speeds. This game-theoretic approach is general enough to quantify the security of a molecular program against malicious manipulations of its relative clock speeds. However, this preliminary report focuses on games against nature, games in which the molecular program's opponent perturbs clock speeds randomly (indifferently) according to the probabilities inherent in chemical kinetics.