Natural Computing

, Volume 15, Issue 2, pp 235–244 | Cite as

Minimal output unstable configurations in chemical reaction networks and deciders



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 compute their finite set of minimal output unstable configurations. As a consequence, a relatively large set 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 20(4):279–304, 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.


Chemical reaction network Population protocol Vector addition system Output stability Chemical reaction decider 



We thank Jan Van den Bussche for interesting discussions on CRNs and for useful comments on an earlier version of this paper. We also thank the anonymous reviewers for useful comments on the paper. R.B. is a postdoctoral fellow of the Research Foundation−Flanders (FWO).


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Hasselt University and Transnational University of LimburgDiepenbeekBelgium

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