When considering circuit synthesis, we typically employ a state graph specification, which can be obtained from the Petri net representation (Myers 2004) and is given for the C-element in Fig. 5b. The values in each state correspond to the values of inputs X, Y and output Z, respectively. A * symbol indicates that the corresponding variable is excited by the outgoing transition (and will be changed in the following state). Observe how we can only transition to a state \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1\text {*} 1\text {*} 1$$\end{document}1*1*1 from a state \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$110\text {*}$$\end{document}110* requiring X as 1 and Y as 1. Because this is derived from a 1-bounded Petri net, we can assume that the transitions \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0\text {*}10 \rightarrow 110\text {*}$$\end{document}0*10→110* and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$10\text {*}0 \rightarrow 110\text {*}$$\end{document}10*0→110* do not conflict.Fig. 5Four specifications of a C-element with inputs X, Y and an output Z. a Conventional logic table, where ‘unchanged’ means that the state of the output is the last stable configuration of 1 or 0. b State graph, in which each state denotes a configuration and a transition is caused by the presence of a signal, where * indicates that the signal is excited. c 1-bounded Petri net specifying the Muller C-element. d Timing diagram for the C-element