Abstract
In this paper, we use some observations on the nature of biochemical reactions to derive interesting properties of qualitative biochemical Kripke structures. We show that these characteristics make Kripke structures of biochemical pathways suitable for assumption based distributed model checking. The number of chemical species participating in a biochemical reaction is usually bounded by a small constant. This observation is used to show that the Hamming distance between adjacent states of a qualitative biochemical Kripke structures is bounded. We call such structures as Bounded Hamming Distance Kripke structures (BHDKS). We, then, argue the suitability of assumption based distributed model checking for BHDKS by constructively deriving worst case upper bounds on the size of the fragments of the state space that need to be stored at each distributed node. We also show that the distributed state space can be mapped naturally to a hypercube based distributed architecture. We support our results by experimental evaluation over benchmarks and biochemical pathways from public databases.
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Brim, L., Yorav, K., ŽÃdková, J.: Assumption-based distribution of CTL model checking. International Journal on Software Tools for Technology Transfer (STTT) 7(1), 61–73 (2005)
Brim, L., ŽÃdková, J., Yorav, K.: Using assumptions to distribute CTL model checking. Electr. Notes Theor. Comput. Sci. 68(4) (2002)
Burch, J.R., Clark, E.M., McMillan, K.L., Dill, D.L., Hwang, L.J.: Symbolic model checking: 1020 states and beyond. In: Mitchell, J.C. (ed.) Proceedings of the 5th Annual IEEE Symposium on Logic in Computer Science, Philadelphia, PA, pp. 428–439. IEEE Computer Society Press, Los Alamitos (1990)
Chabrier, N., Fages, F.: Symbolic model checking of biochemical networks. In: Priami, C. (ed.) CMSB 2003. LNCS, vol. 2602, pp. 149–162. Springer, Heidelberg (2003)
Chabrier-Rivier, N., Chiaverini, M., Danos, V., Fages, F., Schächter, V.: Modeling and querying biomolecular interaction networks. Theoretical Computer Science 325(1), 25–44 (2004)
Chabrier-Rivier, N., Fages, F., Soliman, S.: The biochemical abstract machine biocham. In: Danos, V., Schachter, V. (eds.) CMSB 2004. LNCS (LNBI), vol. 3082, pp. 172–191. Springer, Heidelberg (2005)
Clarke, E.M., Grumberg, O., Peled, D.A.: Model Checking. The MIT Press, Cambridge (1999)
Dwyer, M.B. (ed.): SPIN 2001. LNCS, vol. 2057. Springer, Heidelberg (2001)
Karp, P.D., Riley, M., Paley, S.M., Pellegrini-Toole, A.: Ecocyc: an encyclopedia of escherichia coli genes and metabolism. Nucleic Acids Research 24(1), 32–39 (1996)
Karypis, G., Selvakkumaran, N.: Multi-objective hypergraph partitioning algorithms for cut and maximum subdomain degree minimization. In: ICCAD 2003: Proceedings of the 2003 IEEE/ACM international conference on Computer-aided design, Washington, DC, USA, August 18, 2003, p. 726. IEEE Computer Society Press, Los Alamitos (2003)
Krieger, C.J., Zhang, P., Mueller, L.A., Wang, A., Paley, S.M., Arnaud, M., Pick, J., Rhee, S.Y., Karp, P.D.: Metacyc: a multiorganism database of metabolic pathways and enzymes. Nucleic Acids Research 32(Database-Issue), 438–442 (2004)
Soliman, S., Fages, F.: Cmbslib: A library for comparing formalisms and models of biological systems. In: Danos, V., Schachter, V. (eds.) CMSB 2004. LNCS (LNBI), vol. 3082, pp. 231–235. Springer, Heidelberg (2005)
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Jha, S., Shyamasundar, R.K. (2006). Adapting Biochemical Kripke Structures for Distributed Model Checking. In: Priami, C., Ingólfsdóttir, A., Mishra, B., Riis Nielson, H. (eds) Transactions on Computational Systems Biology VII. Lecture Notes in Computer Science(), vol 4230. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11905455_6
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DOI: https://doi.org/10.1007/11905455_6
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