Advertisement

Computing Preimages and Ancestors in Reaction Systems

  • Roberto Barbuti
  • Anna Bernasconi
  • Roberta Gori
  • Paolo Milazzo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11324)

Abstract

In reaction systems, preimages and n-th ancestors are sets of reactants leading to the production of a target set of products in either one or n steps, respectively. Many computational problems on preimages and ancestors, such as finding all minimum-cardinality n-th ancestors, computing their size, or counting them, are intractable. In this paper we propose a characterization of n-th ancestors as a Boolean formula, and we define an operator able to compute such a formula in polynomial time. Our formula can be exploited to solve all preimage and ancestors problems and, therefore, it can be directly used to study their complexity. In particular, we focus on two problems: (i) deciding whether a preimage/n-th ancestor exists (ii) finding a preimage/n-th ancestor of minimal size. Our approach naturally leads to the definition of classes of systems for which such problems can be solved in polynomial time.

Keywords

Reaction systems Ancestor computation Computational complexity Causality relations 

References

  1. 1.
    Ehrenfeucht, A., Rozenberg, G.: Reaction systems. Fundamenta informaticae 75(1–4), 263–280 (2007)MathSciNetzbMATHGoogle Scholar
  2. 2.
    Brijder, R., Ehrenfeucht, A., Main, M.G., Rozenberg, G.: A tour of reaction systems. Int. J. Found. Comput. Sci. 22(7), 1499–1517 (2011)MathSciNetCrossRefGoogle Scholar
  3. 3.
    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).  https://doi.org/10.1007/978-3-319-08019-2_20CrossRefGoogle Scholar
  4. 4.
    Barbuti, R., Bove, P., Gori, R., Levi, F., Milazzo, P.: Simulating gene regulatory networks using reaction systems. In: Proceedings of the 27th International Workshop on Concurrency, Specification and Programming, CS&P 2018 (2018, to appear)Google Scholar
  5. 5.
    Salomaa, A.: Minimal and almost minimal reaction systems. Nat. Comput. 12(3), 369–376 (2013)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Salomaa, A.: Functional constructions between reaction systems and propositional logic. Int. J. Found. Comput. Sci. 24(1), 147–160 (2013)MathSciNetCrossRefGoogle Scholar
  7. 7.
    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
  8. 8.
    Dennunzio, A., Formenti, E., Manzoni, L., Porreca, A.E.: Preimage problems for reaction systems. In: Dediu, A.-H., Formenti, E., Martín-Vide, C., Truthe, B. (eds.) LATA 2015. LNCS, vol. 8977, pp. 537–548. Springer, Cham (2015).  https://doi.org/10.1007/978-3-319-15579-1_42CrossRefzbMATHGoogle Scholar
  9. 9.
    Barbuti, R., Gori, R., Levi, F., Milazzo, P.: Investigating dynamic causalities in reaction systems. Theor. Comput. Sci. 623, 114–145 (2016)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Barbuti, R., Gori, R., Levi, F., Milazzo, P.: Specialized predictor for reaction systems with context properties. In: Proceedings of the 24th International Workshop on Concurrency, Specification and Programming, CS&P, pp. 31–43 (2015)Google Scholar
  11. 11.
    Barbuti, R., Gori, R., Levi, F., Milazzo, P.: Specialized predictor for reaction systems with context properties. Fundamenta Informaticae 147(2–3), 173–191 (2016)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Barbuti, R., Gori, R., Milazzo, P.: Multiset patterns and their application to dynamic causalities in membrane systems. In: Gheorghe, M., Rozenberg, G., Salomaa, A., Zandron, C. (eds.) CMC 2017. LNCS, vol. 10725, pp. 54–73. Springer, Cham (2018).  https://doi.org/10.1007/978-3-319-73359-3_4CrossRefzbMATHGoogle Scholar
  13. 13.
    Barbuti, R., Gori, R., Levi, F., Milazzo, P.: Generalized contexts for reaction systems: definition and study of dynamic causalities. Acta Informatica 55(3), 227–267 (2018)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Barbuti, R., Gori, R., Milazzo, P.: Predictors for flat membrane systems. Theor. Comput. Sci. 736, 79–102 (2018)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Brijder, R., Ehrenfeucht, A., Rozenberg, G.: A note on causalities in reaction systems. ECEASST 30, 1–9 (2010)Google Scholar
  16. 16.
    Gori, R., Levi, F.: Abstract interpretation based verification of temporal properties for bioambients. Inf. Comput. 208(8), 869–921 (2010)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Bodei, C., Gori, R., Levi, F.: An analysis for causal properties of membrane interactions. Electron. Notes Theor. Comput. Sci. 299, 15–31 (2013)CrossRefGoogle Scholar
  18. 18.
    Bodei, C., Gori, R., Levi, F.: Causal static analysis for brane calculi. Theor. Comput. Sci. 587, 73–103 (2015)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Busi, N.: Causality in membrane systems. In: Eleftherakis, G., Kefalas, P., Păun, G., Rozenberg, G., Salomaa, A. (eds.) WMC 2007. LNCS, vol. 4860, pp. 160–171. Springer, Heidelberg (2007).  https://doi.org/10.1007/978-3-540-77312-2_10CrossRefzbMATHGoogle Scholar
  20. 20.
    Hassoun, S., Sasao, T. (eds.): Logic Synthesis and Verification. Kluwer Academic Publishers, Boston (2002)Google Scholar
  21. 21.
    Umans, C., Villa, T., Sangiovanni-Vincentelli, A.L.: Complexity of two-level logic minimization. IEEE Trans. CAD Integr. Circuits Syst. 25(7), 1230–1246 (2006)CrossRefGoogle Scholar
  22. 22.
    Brayton, R.K., Sangiovanni-Vincentelli, A.L., McMullen, C.T., Hachtel, G.D.: Logic Minimization Algorithms for VLSI Synthesis. Kluwer Academic Publishers, Norwell (1984)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Dipartimento di InformaticaUniversità di PisaPisaItaly

Personalised recommendations