Synthesis of Probability Theory Based on Molecular Computation

Considering the common knowledge that probability theory has long been used to explain stochastic behaviors of chemical reactions, this paper devotes itself to synthesizing probability theory based on molecular computation. Exploring and utilizing the dynamic properties of molecular reactions, this paper proposes an easily understood but systematic method to solve law-of-total-probability-relevant problems within the realm of probability theory. The essence of our proposal could meanwhile be utilized to tackle problems with regard to Bayes' Theorem and Markov chains. Numerial results based on law of mass action have demonstrated and validated the robustness and accuracy of this method. It is worth noting that an already mathematically proven conclusion, which states that nearly an arbitrary set of bimolecular reactions can be implemented by DNA strand displacement reactions, ensures the meaningfulness of our work.