# Democratic, existential, and consensus-based output conventions in stable computation by chemical reaction networks

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## Abstract

We show that some natural output conventions for error-free computation in chemical reaction networks (CRN) lead to a common level of computational expressivity. Our main results are that the standard consensus-based output convention have equivalent computational power to (1) *existence-based* and (2) *democracy-based* output conventions. The CRNs using the former output convention have only “yes” voters, with the interpretation that the CRN’s output is yes if any voters are present and no otherwise. The CRNs using the latter output convention define output by majority vote among “yes” and “no” voters. Both results are proven via a generalized framework that simultaneously captures several definitions, directly inspired by a Petri net result of Esparza, Ganty, Leroux, and Majumder [CONCUR 2015]. These results support the thesis that the computational expressivity of error-free CRNs is intrinsic, not sensitive to arbitrary definitional choices.

### Keywords

Population protocols Chemical reaction networks Stable computation Semilinear predicates## Notes

### Acknowledgements

R.B. thanks Grzegorz Rozenberg for useful comments on an earlier version of this paper and for useful discussions regarding CRNs in general. D.D. thanks Ryan James for suggesting the democratic CRD model. The authors are grateful to anonymous reviewers for comments on a conference version of this paper and on an earlier version of this journal paper that have helped improve the presentation.

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