Robustness of expressivity in chemical reaction networks

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 definition of error-free CRNs have equivalent computational power to 1) asymmetric and 2) democratic CRNs. The former have only "yes" voters, with the interpretation that the CRN's output is yes if any voters are present and no otherwise. The latter 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 recent 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.