Output Stability and Semilinear Sets in Chemical Reaction Networks and Deciders

Abstract

We study the set of output stable configurations of chemical reaction deciders (CRDs). It turns out that CRDs with only bimolecular reactions (which are almost equivalent to population protocols) have a special structure that allows for an algorithm to efficiently calculate the (finite) set of minimal output stable configurations. As a consequence, a relatively large sequence of configurations may be efficiently checked for output stability. We also provide a number of observations regarding the semilinearity result of Angluin et al. [Distrib. Comput., 2007] from the context of population protocols (which is a central result for output stable CRDs). In particular, we observe that the computation-friendly class of totally stable CRDs has equal expressive power as the larger class of output stable CRDs.