Reaction Mining for Reaction Systems

  • Artur Męski
  • Maciej Koutny
  • Wojciech Penczek
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10867)


Reaction systems are a formal model for specifying and analysing computational processes in which reactions operate on sets of entities (molecules), providing a framework for dealing with qualitative aspects of biochemical systems. This paper is concerned with reaction systems in which entities can have discrete concentrations and reactions operate on multisets of entities, providing a succinct framework for dealing with quantitative aspects of systems. This is facilitated by a dedicated linear-time temporal logic which allows one to express and verify a wide range of behavioural system properties.

In practical applications, a reaction system with discrete concentrations may only be partially specified, and effective calculation of the missing details would provide an attractive design approach. To develop such an approach, this paper introduces reaction systems with parameters representing the unknown parts of the reactions. The main result is a method which attempts to replace these parameters in such a way that the resulting reaction system operating in a given external environment satisfies a given temporal logic formula. We provide a suitable encoding of parametric reaction systems in smt, and outline a synthesis procedure based on bounded model checking for solving the synthesis problem. We also provide preliminary experimental results demonstrating the feasibility of the new synthesis method.



W. Penczek acknowledges the support of the National Centre for Research and Development (NCBR), Poland, under the PolLux project VoteVerif (POL-LUX-IV/1/2016).


  1. 1.
    Alhazov, A., Aman, B., Freund, R., Ivanov, S.: Simulating R systems by P systems. In: Leporati, A., Rozenberg, G., Salomaa, A., Zandron, C. (eds.) CMC 2016. LNCS, vol. 10105, pp. 51–66. Springer, Cham (2017). Scholar
  2. 2.
    Azimi, S., Gratie, C., Ivanov, S., Manzoni, L., Petre, I., Porreca, A.E.: Complexity of model checking for reaction systems. Theor. Comput. Sci. 623, 103–113 (2016)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Azimi, S., Gratie, C., Ivanov, S., Petre, I.: Dependency graphs and mass conservation in reaction systems. Theor. Comput. Sci. 598, 23–39 (2015)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Azimi, S., Iancu, B., Petre, I.: Reaction system models for the heat shock response. Fundamenta Informaticae 131(3–4), 299–312 (2014)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Brijder, R., Ehrenfeucht, A., Rozenberg, G.: Reaction systems with duration. In: Kelemen, J., Kelemenová, A. (eds.) Computation, Cooperation, and Life. LNCS, vol. 6610, pp. 191–202. Springer, Heidelberg (2011). Scholar
  6. 6.
    Corolli, L., Maj, C., Marini, F., Besozzi, D., Mauri, G.: An excursion in reaction systems: from computer science to biology. Theor. Comput. Sci. 454, 95–108 (2012)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Dennunzio, A., Formenti, E., Manzoni, L.: Reaction systems and extremal combinatorics properties. Theor. Comput. Sci. 598, 138–149 (2015)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Dennunzio, A., Formenti, E., Manzoni, L., Porreca, A.E.: Ancestors, descendants, and gardens of eden in reaction systems. Theor. Comput. Sci. 608, 16–26 (2015)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Ehrenfeucht, A., Kleijn, J., Koutny, M., Rozenberg, G.: Reaction systems: a natural computing approach to the functioning of living cells. In: A Computable Universe, Understanding and Exploring Nature as Computation, pp. 189–208 (2012)CrossRefGoogle Scholar
  10. 10.
    Ehrenfeucht, A., Kleijn, J., Koutny, M., Rozenberg, G.: Evolving reaction systems. Theor. Comput. Sci. 682, 79–99 (2017)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Ehrenfeucht, A., Rozenberg, G.: Reaction systems. Fundamenta Informaticae 75(1–4), 263–280 (2007)MathSciNetzbMATHGoogle Scholar
  12. 12.
    Ehrenfeucht, A., Rozenberg, G.: Introducing time in reaction systems. Theor. Comput. Sci. 410(4–5), 310–322 (2009)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Formenti, E., Manzoni, L., Porreca, A.E.: Cycles and global attractors of reaction systems. In: Jürgensen, H., Karhumäki, J., Okhotin, A. (eds.) DCFS 2014. LNCS, vol. 8614, pp. 114–125. Springer, Cham (2014). Scholar
  14. 14.
    Formenti, E., Manzoni, L., Porreca, A.E.: Fixed points and attractors of reaction systems. In: Beckmann, A., Csuhaj-Varjú, E., Meer, K. (eds.) CiE 2014. LNCS, vol. 8493, pp. 194–203. Springer, Cham (2014). Scholar
  15. 15.
    Formenti, E., Manzoni, L., Porreca, A.E.: On the complexity of occurrence and convergence problems in reaction systems. Nat. Comput. 14, 1–7 (2014)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Hirvensalo, M.: On probabilistic and quantum reaction systems. Theor. Comput. Sci. 429, 134–143 (2012)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Horn, F., Jackson, R.: General mass action kinetics. Arch. Ration. Mech. Anal. 47(2), 81–116 (1972)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Kroening, D., Strichman, O.: Decision Procedures - An Algorithmic Point of View. Texts in Theoretical Computer Science. An EATCS Series, 2nd edn. Springer, Heidelberg (2016). Scholar
  19. 19.
    Męski, A., Koutny, M., Penczek, W.: Towards quantitative verification of reaction systems. In: Amos, M., Condon, A. (eds.) UCNC 2016. LNCS, vol. 9726, pp. 142–154. Springer, Cham (2016). Scholar
  20. 20.
    Męski, A., Penczek, W., Rozenberg, G.: Model checking temporal properties of reaction systems. Inf. Sci. 313, 22–42 (2015)CrossRefGoogle Scholar
  21. 21.
    de Moura, L., Bjørner, N.: Z3: an efficient SMT solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337–340. Springer, Heidelberg (2008). Scholar
  22. 22.
    Męski, A., Koutny, M., Penczek, W.: Verification of linear-time temporal properties for reaction systems with discrete concentrations. Fundam. Inform. 154(1–4), 289–306 (2017)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Salomaa, A.: Functions and sequences generated by reaction systems. Theor. Comput. Sci. 466, 87–96 (2012)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Salomaa, A.: On state sequences defined by reaction systems. In: Constable, R.L., Silva, A. (eds.) Logic and Program Semantics. LNCS, vol. 7230, pp. 271–282. Springer, Heidelberg (2012). Scholar
  25. 25.
    Salomaa, A.: Functional constructions between reaction systems and propositional logic. Int. J. Found. Comput. Sci. 24(1), 147–160 (2013)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Salomaa, A.: Minimal and almost minimal reaction systems. Nat. Comput. 12(3), 369–376 (2013)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Artur Męski
    • 1
    • 2
  • Maciej Koutny
    • 3
  • Wojciech Penczek
    • 1
    • 4
  1. 1.Institute of Computer SciencePASWarsawPoland
  2. 2.Vector GB LimitedLondonUK
  3. 3.School of ComputingNewcastle UniversityNewcastle upon TyneUK
  4. 4.Faculty of Science, Institute of Computer ScienceSiedlce UniversitySiedlcePoland

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