Dual-rail representation We represent a Boolean circuit with inputs I and outputs O, denoted B(I, O), as follows. Firstly, a Boolean variable \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b=\{0,1\}$$\end{document}b={0,1} could be encoded in a single species X, where 0 would be encoded as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E[|X|] = 0$$\end{document}E[|X|]=0 and 1 as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E[|X|] \ge M$$\end{document}E[|X|]≥M, where E[|X|] denotes an expectation of the number of molecules of X and M is a molecular population threshold.