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Reachability in Deletion-Only Chemical Reaction Networks

Authors Bin Fu, Timothy Gomez, Ryan Knobel, Austin Luchsinger, Aiden Massie, Marco Rodriguez, Adrian Salinas, Robert Schweller, Tim Wylie

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Subject Classification

ACM Subject Classification
  • Theory of computation → Models of computation
  • Theory of computation → Problems, reductions and completeness
Keywords
  • CRN
  • Chemical Reaction Network
  • Reachability
  • Void Reactions

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Abstract

For general discrete Chemical Reaction Networks (CRNs), the fundamental problem of reachability - the question of whether a target configuration can be produced from a given initial configuration - was recently shown to be Ackermann-complete. However, many open questions remain about which features of the CRN model drive this complexity. We study a restricted class of CRNs with void rules, reactions that only decrease species counts. We further examine this regime in the motivated model of step CRNs, which allow additional species to be introduced in discrete stages. With and without steps, we characterize the complexity of the reachability problem for CRNs with void rules. We show that, without steps, reachability remains polynomial-time solvable for bimolecular systems but becomes NP-complete for larger reactions. Conversely, with just a single step, reachability becomes NP-complete even for bimolecular systems. Our results provide a nearly complete classification of void-rule reachability problems into tractable and intractable cases, with only a single exception.

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Bin Fu, Timothy Gomez, Ryan Knobel, Austin Luchsinger, Aiden Massie, Marco Rodriguez, Adrian Salinas, Robert Schweller, and Tim Wylie. Reachability in Deletion-Only Chemical Reaction Networks. In 31st International Conference on DNA Computing and Molecular Programming (DNA 31). Leibniz International Proceedings in Informatics (LIPIcs), Volume 347, pp. 3:1-3:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.DNA.31.3

Author Details

Bin Fu
  • University of Texas Rio Grande Valley, Edinburg, TX, USA
Timothy Gomez
  • Massachusetts Institute of Technology, Cambridge, MA, USA
Ryan Knobel
  • University of Texas Rio Grande Valley, Edinburg, TX, USA
Austin Luchsinger
  • University of Texas Rio Grande Valley, Edinburg, TX, USA
Aiden Massie
  • University of Texas Rio Grande Valley, Edinburg, TX, USA
Marco Rodriguez
  • Massachusetts Institute of Technology, Cambridge, MA, USA
Adrian Salinas
  • University of Texas Rio Grande Valley, Edinburg, TX, USA
Robert Schweller
  • University of Texas Rio Grande Valley, Edinburg, TX, USA
Tim Wylie
  • University of Texas Rio Grande Valley, Edinburg, TX, USA

Funding

This research was supported in part by National Science Foundation Grant CCF-2329918.

References

  1. Robert M. Alaniz, Bin Fu, Timothy Gomez, Elise Grizzell, Andrew Rodriguez, Robert Schweller, and Tim Wylie. Reachability in restricted chemical reaction networks, 2022. URL: https://doi.org/10.48550/arXiv.2211.12603.
  2. Rachel Anderson, Alberto Avila, Bin Fu, Timothy Gomez, Elise Grizzell, Aiden Massie, Gourab Mukhopadhyay, Adrian Salinas, Robert Schweller, Evan Tomai, and Tim Wylie. Computing threshold circuits with void reactions in step chemical reaction networks. In 10th conference on Machines, Computations and Universality (MCU 2024), 2024. Google Scholar
  3. Rachel Anderson, Bin Fu, Aiden Massie, Gourab Mukhopadhyay, Adrian Salinas, Robert Schweller, Evan Tomai, and Tim Wylie. Computing threshold circuits with bimolecular void reactions in step chemical reaction networks. In International Conference on Unconventional Computation and Natural Computation, pages 253-268. Springer, 2024. URL: https://doi.org/10.1007/978-3-031-63742-1_18.
  4. Dana Angluin, James Aspnes, Zoë Diamadi, Michael J. Fischer, and René Peralta. Computation in networks of passively mobile finite-state sensors. Distributed Computing, 18(4):235-253, March 2006. URL: https://doi.org/10.1007/s00446-005-0138-3.
  5. Rutherford Aris. Prolegomena to the rational analysis of systems of chemical reactions. Archive for Rational Mechanics and Analysis, 19(2):81-99, January 1965. URL: https://doi.org/10.1007/BF00282276.
  6. Rutherford Aris. Prolegomena to the rational analysis of systems of chemical reactions ii. some addenda. Archive for Rational Mechanics and Analysis, 27(5):356-364, January 1968. URL: https://doi.org/10.1007/BF00251438.
  7. Michael Blondin, Matthias Englert, Alain Finkel, Stefan Göller, Christoph Haase, Ranko Lazić, Pierre Mckenzie, and Patrick Totzke. The reachability problem for two-dimensional vector addition systems with states. Journal of the ACM (JACM), 68(5):1-43, 2021. URL: https://doi.org/10.1145/3464794.
  8. Adam Case, Jack H Lutz, and Donald M Stull. Reachability problems for continuous chemical reaction networks. Natural Computing, 17(2):223-230, 2018. URL: https://doi.org/10.1007/S11047-017-9641-2.
  9. Matthew Cook, David Soloveichik, Erik Winfree, and Jehoshua Bruck. Programmability of Chemical Reaction Networks, pages 543-584. Springer Berlin Heidelberg, Berlin, Heidelberg, 2009. URL: https://doi.org/10.1007/978-3-540-88869-7_27.
  10. Wojciech Czerwiński, Sławomir Lasota, Ranko Lazić, Jérôme Leroux, and Filip Mazowiecki. The reachability problem for Petri nets is not elementary. Journal of the ACM (JACM), 68(1):1-28, 2020. URL: https://doi.org/10.1145/3422822.
  11. Wojciech Czerwiński, Sławomir Lasota, and Łukasz Orlikowski. Improved Lower Bounds for Reachability in Vector Addition Systems. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021), volume 198 of Leibniz International Proceedings in Informatics (LIPIcs), pages 128:1-128:15, Dagstuhl, Germany, 2021. Schloss Dagstuhl - Leibniz-Zentrum für Informatik. URL: https://doi.org/10.4230/LIPIcs.ICALP.2021.128.
  12. Wojciech Czerwiński and Łukasz Orlikowski. Reachability in vector addition systems is Ackermann-complete. In 62nd Annual Symposium on Foundations of Computer Science, FOCS'21, pages 1229-1240. IEEE, 2021. Google Scholar
  13. Daniel T Gillespie. Stochastic simulation of chemical kinetics. Annu. Rev. Phys. Chem., 58(1):35-55, 2007. Google Scholar
  14. Michel Henri Théodore Hack. Decidability questions for Petri Nets. PhD thesis, Massachusetts Institute of Technology, 1976. Google Scholar
  15. John Hopcroft and Jean-Jacques Pansiot. On the reachability problem for 5-dimensional vector addition systems. Theoretical Computer Science, 8(2):135-159, 1979. URL: https://doi.org/10.1016/0304-3975(79)90041-0.
  16. Richard M. Karp and Raymond E. Miller. Parallel program schemata. Journal of Computer and System Sciences, 3(2):147-195, 1969. URL: https://doi.org/10.1016/S0022-0000(69)80011-5.
  17. Ulla Koppenhagen and Ernst W Mayr. Optimal algorithms for the coverability, the subword, the containment, and the equivalence problems for commutative semigroups. Information and Computation, 158(2):98-124, 2000. URL: https://doi.org/10.1006/INCO.1999.2812.
  18. Jérôme Leroux. The reachability problem for Petri nets is not primitive recursive. In 62nd Annual Symposium on Foundations of Computer Science, FOCS'21. IEEE, 2021. Google Scholar
  19. Jérôme Leroux and Sylvain Schmitz. Reachability in vector addition systems is primitive-recursive in fixed dimension. In 2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), pages 1-13. IEEE, 2019. URL: https://doi.org/10.1109/LICS.2019.8785796.
  20. Richard J. Lipton. The reachability problem requires exponential space. Technical Report 62, Yale University, 1976. Google Scholar
  21. Ernst W. Mayr. An algorithm for the general Petri net reachability problem. In Proceedings of the Thirteenth Annual ACM Symposium on Theory of Computing, STOC '81, pages 238-246, New York, NY, USA, 1981. Association for Computing Machinery. URL: https://doi.org/10.1145/800076.802477.
  22. Ernst W Mayr and Albert R Meyer. The complexity of the word problems for commutative semigroups and polynomial ideals. Advances in mathematics, 46(3):305-329, 1982. Google Scholar
  23. Carl Adam Petri. Kommunikation mit Automaten. PhD thesis, Rheinisch-Westfälischen Institutes für Instrumentelle Mathematik an der Universität Bonn, 1962. Google Scholar
  24. Ján Plesník. The np-completeness of the hamiltonian cycle problem in planar diagraphs with degree bound two. Information Processing Letters, 8(4):199-201, 1979. URL: https://doi.org/10.1016/0020-0190(79)90023-1.
  25. George S Sacerdote and Richard L Tenney. The decidability of the reachability problem for vector addition systems (preliminary version). In Proceedings of the ninth annual ACM symposium on Theory of computing, pages 61-76, 1977. URL: https://doi.org/10.1145/800105.803396.
  26. Sylvain Schmitz. The complexity of reachability in vector addition systems. ACM SigLog News, 2016. URL: https://doi.org/10.1145/2893582.2893585.
  27. David Soloveichik, Matthew Cook, Erik Winfree, and Jehoshua Bruck. Computation with finite stochastic chemical reaction networks. natural computing, 7(4):615-633, 2008. URL: https://doi.org/10.1007/S11047-008-9067-Y.
  28. Gergely Szlobodnyik and Gábor Szederkényi. Polynomial time reachability analysis in discrete state chemical reaction networks obeying conservation laws. MATCH-Communications in Mathematical and in Computer Chemistry, 89(1):175-196, 2023. Google Scholar
  29. Gergely Szlobodnyik, Gábor Szederkényi, and Matthew D Johnston. Reachability analysis of subconservative discrete chemical reaction networks. MATCH-Communications in Mathematical and in Computer Chemistry, 81(3):705-736, 2019. Google Scholar
  30. Robert Tarjan. Depth-first search and linear graph algorithms. SIAM journal on computing, 1(2):146-160, 1972. URL: https://doi.org/10.1137/0201010.
  31. Chris Thachuk and Anne Condon. Space and energy efficient computation with dna strand displacement systems. In International Workshop on DNA-Based Computers, 2012. Google Scholar
  32. Boya Wang, Chris Thachuk, Andrew D Ellington, Erik Winfree, and David Soloveichik. Effective design principles for leakless strand displacement systems. Proceedings of the National Academy of Sciences, 115(52):E12182-E12191, 2018. Google Scholar
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