Minimal output unstable configurations in chemical reaction networks and deciders
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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.
KeywordsChemical 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).
- Angluin D, Aspnes J, Eisenstat D (2006) Stably computable predicates are semilinear. In: Ruppert E, Malkhi D (eds) Proceedings of the 25th annual ACM symposium on principles of distributed computing (PODC 2006). ACM, pp 292–299Google Scholar
- Brijder R (2014) Output stability and semilinear sets in chemical reaction networks and deciders. In: Murata S, Kobayashi S (eds) Proceedings of the 20th international conference on DNA computing and molecular programming (DNA 20), volume 8727 of lecture notes in computer science. Springer, pp 100–113Google Scholar
- Chen H-L, Doty D, Soloveichik D (2012) Deterministic function computation with chemical reaction networks. In: Stefanovic D, Turberfield AJ (eds) Proceedings of the 18th international conference on DNA computing and molecular programming (DNA 18), volume 7433 of lecture notes in computer science. Springer, pp 25–42Google Scholar
- Chen H-L, Doty D, Soloveichik D (2014) Rate-independent computation in continuous chemical reaction networks. In: Naor M (ed) Innovations in theoretical computer science (ITCS’14). ACM, pp 313–326Google Scholar
- Doty D (2014) Timing in chemical reaction networks. In: Chekuri C (ed) Proceedings of the 25th annual ACM–SIAM symposium on discrete algorithms (SODA 2014). SIAM, pp 772–784Google Scholar
- Doty D, Hajiaghayi M (2013) Leaderless deterministic chemical reaction networks. In: Soloveichik D, Yurke B (eds) Proceedings of the 19th international conference on DNA computing and molecular programming (DNA 19), volume 8141 of lecture notes in computer science. Springer, pp 46–60Google Scholar
- Leroux J (2012) Vector addition systems reachability problem (a simpler solution). In: Voronkov A (ed) Proceedings of the Alan Turing centenary conference (Turing-100), volume 10 of EPiC series, pp 214–228Google Scholar
- Mayr EW (1981) An algorithm for the general Petri net reachability problem. In: Proceedings of the 13th annual ACM symposium on theory of computing (STOC ’81). ACM, New York, NY, USA, pp 238–246Google Scholar
- Plotkin GD (2013) A calculus of chemical systems. In: Tannen V, Wong L, Libkin L, Fan W, Tan W-C, Fourman M (eds) In search of elegance in the theory and practice of computation, volume 8000 of lecture notes in computer science. Springer, Berlin, Heidelberg, pp 445–465Google Scholar