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===Generalization for multiple-valued logic===
The definition of C-element can be generalized for multiple-valued logic,<ref name="Kim69" /><ref>[https://www.proquest.com/docview/303676273?pq-origsite=gscholar&fromopenview=true J. M. Johnson, Theory and Application of Self-Timed Integrated Systems Using Ternary Logic Elements. PhD thesis. University of California, Santa Barbara. 1989.]</ref>,<ref>[https://glim-re.repo.nii.ac.jp/record/3834/files/thesis_O79.pdf H. Sato, Completeness on Multiple-Valued Logical Functions Realized by Asynchronous Sequential Circuits. PhD thesis, Gakushuin University, 1996.]</ref> or even for continuous signals:
:<math>\text { if } x_1=x_2=...=x_m, \text { then } y_n=\text{any}(x_1,x_2,...,x_m), \text { else } y_n=y_{n-1}.</math>
For example, the truth table for a balanced ternary C-element with two inputs is
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