Democratic, Existential, and Consensus-Based Output Conventions in Stable Computation by Chemical Reaction Networks

TL;DR

This paper demonstrates that different natural output conventions in error-free chemical reaction networks have equivalent computational power, indicating that the expressivity of such CRNs is intrinsic and not dependent on the specific output definition used.

Contribution

It proves the equivalence in computational power among consensus-based, existence-based, and democracy-based output conventions in error-free CRNs.

Findings

Consensus, existence, and democracy output conventions are computationally equivalent.

CRNs with 'yes' voters only can decide 'yes' or 'no' based on voter presence.

Majority voting in CRNs is as powerful as other output conventions.

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.