A New Occurrence Counting Analysis for BioAmbients

  • Roberta Gori
  • Francesca Levi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3780)


This paper concerns the application of formal methods to biological systems, modelled specifically in BioAmbients [30]. BioAmbients [30] is a variant of the Mobile Ambients (MA) [7] calculus, designed precisely for more faithfully capturing basic biological concepts. We propose a new static analysis for BioAmbients which computes approximate information about the run-time behaviour of a system. The analysis is derived following the abstract interpretation approach and introduces two main novelties with respect to the analyses in literature [25,24,26,27]: (i) it records information about the number of occurrences of objects; (ii) it maintains more detailed information about the possible contents of ambients, at any time. In this way, the analysis gives substantially more precise results and captures both the quantitative and causal aspect which are really important for reasoning on the temporal and spatial structure of biological systems. The interest of the analysis is demonstrated by considering a few simple examples which point out the limitations of the existing analyses for BioAmbients.


Mobile Ambients and BioAmbients calculus static analysis abstract interpretation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Amtoft, T.: Causal Type System for Ambient Movements. Submitted for publication (2003)Google Scholar
  2. 2.
    Amtoft, T., Kfoury, A.J., Pericas-Geertsen, S.M.: What are Polymorphically-Typed Ambients? In: Sands, D. (ed.) ESOP 2001. LNCS, vol. 2028, pp. 206–220. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  3. 3.
    Amtoft, T., Makholm, H., Wells, J.B.: PolyA: True Type Polymorphism for Mobile Ambients. In: Proc. of TCS 2004, pp. 591–604. Kluwer, Dordrecht (2004)Google Scholar
  4. 4.
    Barbuti, R., Cataudella, S., Maggiolo-Schettini, A., Milazzo, P., Troina, A.: A Probabilistic Calculus for Molecular Systems. In: Proc. of Workshop CS & P, Informatik Berichte, vol. 170, pp. 202–216. Humboldt University press (2004)Google Scholar
  5. 5.
    Bodei, C., Degano, P., Priami, C., Zannone, N.: An enhanced cfa for security policies. In: Proc. of WITS 2003 (2003)Google Scholar
  6. 6.
    Dignum, F.P.M., Cortés, U. (eds.): AMEC 2000. LNCS (LNAI), vol. 2003. Springer, Heidelberg (2001)zbMATHGoogle Scholar
  7. 7.
    Cardelli, L., Gordon, A.D.: Mobile ambients. Theoretical Computer Science 240, 177–213 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Chabrier, N., Fages, F.: Symbolic model-checking of biochemical networks. In: Proceedings of the First International Workshop on Computational Methods in Systems Biology, pp. 149–162 (2003)Google Scholar
  9. 9.
    Cousot, P., Cousot, R.: Abstract Interpretation: A Unified Lattice Model for Static Analysis of Programs by Construction or Approximation of Fixpoints. In: Proc. Fourth ACM Symp. Principles of Programming Languages, pp. 238–252 (1977)Google Scholar
  10. 10.
    Cousot, P., Cousot, R.: Systematic Design of Program Analysis Frameworks. In: Proc. Sixth ACM Symp. Principles of Programming Languages, pp. 269–282 (1979)Google Scholar
  11. 11.
    Cousot, P., Cousot, R.: Comparing the Galois Connection and Widening/Narrowing Approaches to Abstract Interpretation. In: Bruynooghe, M., Wirsing, M. (eds.) PLILP 1992. LNCS, vol. 631, pp. 269–295. Springer, Heidelberg (1992)CrossRefGoogle Scholar
  12. 12.
    Degano, P., Levi, F., Bodei, C.: Safe Ambients: Control Flow Analysis and Security. In: He, J., Sato, M. (eds.) ASIAN 2000. LNCS, vol. 1961, pp. 199–214. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  13. 13.
    Feret, J.: Abstract Interpretation-Based Static Analysis of Mobile Ambients. In: Cousot, P. (ed.) SAS 2001. LNCS, vol. 2126, pp. 412–430. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  14. 14.
    Hansen, R.R., Jensen, J.G., Nielson, F., Nielson, H.R.: Abstract Interpretation of Mobile Ambients. In: Cortesi, A., Filé, G. (eds.) SAS 1999. LNCS, vol. 1694, pp. 134–148. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  15. 15.
    Kam, N., Harel, D., Kugler, H., Marelly, R., Pnueli, A., Hubbard, E.J.A., Stern, M.J.: Formal Modeling of C. elegans Development: A Scenario-Based Approach. In: Priami, C. (ed.) CMSB 2003. LNCS, vol. 2602, pp. 4–20. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  16. 16.
    Hofestadt, R., Thelen, S.: Quantitative modeling of biochemical networks. Silico Biology 1, 39–53 (1998)Google Scholar
  17. 17.
    Levi, F., Maffeis, S.: On Abstract Interpretation of Mobile Ambients. Information and Computation 188, 179–240 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Levi, F., Sangiorgi, D.: Mobile Safe Ambients. TOPLAS 25(1), 1–69 (2003)CrossRefGoogle Scholar
  19. 19.
    Mardare, R., Priami, C.: Logical Analysis of Biological Systems. Fundamenta Informaticae 64, 271–285 (2005)MathSciNetGoogle Scholar
  20. 20.
    Mardare, R., Vagin, O., Quaglia, P., Priami, C.: Model Checking Biological Systems described using Ambient Calculus. In: Danos, V., Schachter, V. (eds.) CMSB 2004. LNCS (LNBI), vol. 3082, pp. 85–103. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  21. 21.
    Matsuno, H., Doi, A., Nagasaki, M., Miyano, S.: Hybrid petri net representation of gene regulatory network. In: Pacific Symposium on Biocomputing, vol. (5), pp. 338–349 (2000)Google Scholar
  22. 22.
    Milner, R., Parrow, J., Walker, D.: A Calculus of Mobile Processes. Information and Computation 100, 1–77 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    Nielson, F., Nielson, H.R., Hansen, R.R.: Validating firewalls using flow logics. Theoretical Computer Science 283(2), 381–418 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    Nielson, F., Nielson, H.R., Pilegaard, H.: Spatial Analysis of BioAmbients. In: Giacobazzi, R. (ed.) SAS 2004. LNCS, vol. 3148, pp. 69–83. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  25. 25.
    Nielson, F., Nielson, H.R., Priami, C., Schuch da Rosa, D.: Control Flow Analysis for BioAmbients. In: BioCONCUR 2003. Electronic Notes in Computer Science (2003)Google Scholar
  26. 26.
    Nielson, F., Nielson, H.R., Priami, C., Schuch da Rosa, D.: Static Analysis for Systems Biology. In: Proc. of the winter International Symposium on Information and Communication Technologies, Trinity College Dublin, pp. 1–6 (2004)Google Scholar
  27. 27.
    Pilegaard, H., Nielson, F., Nielson, H.R.: Static Analysis of a Model of the LDL Degradation Pathway. In: Proc. of CMSB 2005 (2005) (to appear)Google Scholar
  28. 28.
    Priami, C., Quaglia, P.: Beta binders for biological interactions. In: Danos, V., Schachter, V. (eds.) CMSB 2004. LNCS (LNBI), vol. 3082, pp. 20–33. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  29. 29.
    Priami, C., Regev, A., Silverman, W., Shapiro, E.: Application of a stochastic name-passing calculus to representation and simulation of molecular processes. Information Processing Letters 80(1), 25–31 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  30. 30.
    Regev, A., Panina, E.M., Silverman, W., Cardelli, L., Shapiro, E.: BioAmbients: an Abstraction for Biological Compartments. Theoretical Computer Science 325, 141–167 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  31. 31.
    Regev, A., Silverman, W., Shapiro, E.: Representation and Simulation of Biochemical Processes using the pi-calculus process algebra. In: Proc. of the Pacific Symposium on Biocomputing 2001, vol. 6, pp. 459–470 (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Roberta Gori
    • 1
  • Francesca Levi
    • 2
  1. 1.Department of Computer ScienceUniversity of PisaItaly
  2. 2.DISIUniversity of GenovaItaly

Personalised recommendations