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On the Runtime of Chemical Reaction Networks Beyond Idealized Conditions

Authors Anne Condon, Yuval Emek, Noga Harlev

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Anne Condon
  • University of British Columbia, Vancouver, Canada
Yuval Emek
  • Technion - Israel Institute of Technology, Haifa, Israel
Noga Harlev
  • Technion - Israel Institute of Technology, Haifa, Israel

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Anne Condon, Yuval Emek, and Noga Harlev. On the Runtime of Chemical Reaction Networks Beyond Idealized Conditions. In 29th International Conference on DNA Computing and Molecular Programming (DNA 29). Leibniz International Proceedings in Informatics (LIPIcs), Volume 276, pp. 3:1-3:22, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


This paper studies the (discrete) chemical reaction network (CRN) computational model that emerged in the last two decades as an abstraction for molecular programming. The correctness of CRN protocols is typically established under one of two possible schedulers that determine how the execution advances: (1) a stochastic scheduler that obeys the (continuous time) Markov process dictated by the standard model of stochastic chemical kinetics; or (2) an adversarial scheduler whose only commitment is to maintain a certain fairness condition. The latter scheduler is justified by the fact that the former one crucially assumes "idealized conditions" that more often than not, do not hold in real wet-lab experiments. However, when it comes to analyzing the runtime of CRN protocols, the existing literature focuses strictly on the stochastic scheduler, thus raising the research question that drives this work: Is there a meaningful way to quantify the runtime of CRNs without the idealized conditions assumption? The main conceptual contribution of the current paper is to answer this question in the affirmative, formulating a new runtime measure for CRN protocols that does not rely on idealized conditions. This runtime measure is based on an adapted (weaker) fairness condition as well as a novel scheme that enables partitioning the execution into short rounds and charging the runtime for each round individually (inspired by definitions for the runtime of asynchronous distributed algorithms). Following that, we turn to investigate various fundamental computational tasks and establish (often tight) bounds on the runtime of the corresponding CRN protocols operating under the adversarial scheduler. This includes an almost complete chart of the runtime complexity landscape of predicate decidability tasks.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
  • chemical reaction networks
  • adversarial runtime
  • weak fairness
  • predicate decidability


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  1. Dan Alistarh, Bartłomiej Dudek, Adrian Kosowski, David Soloveichik, and Przemysław Uznański. Robust detection in leak-prone population protocols. In DNA Computing and Molecular Programming: 23rd International Conference, DNA 23, Austin, TX, USA, September 24-28, 2017, Proceedings 23, pages 155-171. Springer, 2017. Google Scholar
  2. Dana Angluin, James Aspnes, Zoë Diamadi, Michael J. Fischer, and René Peralta. Computation in networks of passively mobile finite-state sensors. Distributed Comput., 18(4):235-253, 2006. Google Scholar
  3. Dana Angluin, James Aspnes, and David Eisenstat. Fast computation by population protocols with a leader. Distributed Comput., 21(3):183-199, 2008. Google Scholar
  4. Dana Angluin, James Aspnes, David Eisenstat, and Eric Ruppert. The computational power of population protocols. Distrib. Comput., 20(4):279-304, 2007. Google Scholar
  5. James Aspnes and Eric Ruppert. An introduction to population protocols. In Benoît Garbinato, Hugo Miranda, and Luís E. T. Rodrigues, editors, Middleware for Network Eccentric and Mobile Applications, pages 97-120. Springer, 2009. Google Scholar
  6. Baruch Awerbuch. Complexity of network synchronization. J. ACM, 32(4):804-823, October 1985. URL:
  7. Hamid Bolouri and James M. Bower. Computational Modeling of Genetic and Biochemical Networks. The MIT Press, February 2001. URL:
  8. Robert Brijder. Minimal output unstable configurations in chemical reaction networks and deciders. Nat. Comput., 15(2):235-244, 2016. Google Scholar
  9. Robert Brijder. Computing with chemical reaction networks: a tutorial. Nat. Comput., 18(1):119-137, 2019. Google Scholar
  10. Ho-Lin Chen, Rachel Cummings, David Doty, and David Soloveichik. Speed faults in computation by chemical reaction networks. Distributed Comput., 30(5):373-390, 2017. Google Scholar
  11. Ho-Lin Chen, David Doty, and David Soloveichik. Deterministic function computation with chemical reaction networks. Nat. Comput., 13(4):517-534, 2014. Google Scholar
  12. Anne Condon. On design and analysis of chemical reaction network algorithms. In Cezar Câmpeanu, editor, Implementation and Application of Automata - 23rd International Conference, CIAA 2018, Charlottetown, PE, Canada, July 30 - August 2, 2018, Proceedings, volume 10977 of Lecture Notes in Computer Science, pages 1-3. Springer, 2018. Google Scholar
  13. Anne Condon, Yuval Emek, and Noga Harlev. On the runtime of crns beyond idealized conditions, 2023. URL:
  14. Matthew Cook, David Soloveichik, Erik Winfree, and Jehoshua Bruck. Programmability of chemical reaction networks. In Anne Condon, David Harel, Joost N. Kok, Arto Salomaa, and Erik Winfree, editors, Algorithmic Bioprocesses, Natural Computing Series, pages 543-584. Springer, 2009. Google Scholar
  15. Rachel Cummings, David Doty, and David Soloveichik. Probability 1 computation with chemical reaction networks. Nat. Comput., 15(2):245-261, 2016. Google Scholar
  16. S. Dolev, A. Israeli, and S. Moran. Uniform dynamic self-stabilizing leader election. IEEE Transactions on Parallel and Distributed Systems, 8(4):424-440, 1997. URL:
  17. David Doty. Timing in chemical reaction networks. In Chandra Chekuri, editor, Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014, Portland, Oregon, USA, January 5-7, 2014, pages 772-784. SIAM, 2014. Google Scholar
  18. David Doty and Monir Hajiaghayi. Leaderless deterministic chemical reaction networks. Nat. Comput., 14(2):213-223, 2015. Google Scholar
  19. Bartłomiej Dudek and Adrian Kosowski. Universal protocols for information dissemination using emergent signals. In Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing, pages 87-99, 2018. Google Scholar
  20. Daniel T. Gillespie. Exact stochastic simulation of coupled chemical reactions. The Journal of Physical Chemistry, 81(25):2340-2361, 1977. Google Scholar
  21. Richard M. Karp and Raymond E. Miller. Parallel program schemata. J. Comput. Syst. Sci., 3(2):147-195, May 1969. URL:
  22. Othon Michail, Ioannis Chatzigiannakis, and Paul G. Spirakis. New Models for Population Protocols. Synthesis Lectures on Distributed Computing Theory. Morgan & Claypool Publishers, 2011. Google Scholar
  23. Grzegorz Rozenberg and Joost Engelfriet. Elementary net systems, pages 12-121. Springer Berlin Heidelberg, Berlin, Heidelberg, 1998. URL:
  24. David Soloveichik, Matthew Cook, Erik Winfree, and Jehoshua Bruck. Computation with finite stochastic chemical reaction networks. Nat. Comput., 7(4):615-633, 2008. Google Scholar
  25. Marko Vasić, Cameron Chalk, Austin Luchsinger, Sarfraz Khurshid, and David Soloveichik. Programming and training rate-independent chemical reaction networks. Proceedings of the National Academy of Sciences, 119(24):e2111552119, 2022. Google Scholar
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