Probabilistic model checking of biological systems with uncertain kinetic rates

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 5797, Issue , 2009, Pages 64-78

  Barbuti, Roberto ^a   Levi, Francesca ^a   Milazzo, Paolo ^a   Scatena, Guido ^b  

^a UNIVERSITY OF PISA   (Italy)

^b IMT SCHOOL FOR ADVANCED STUDIES LUCCA   (Italy)

Author keywords

Abstract interpretation; Interval Markov chains; Probabilistic model checking; Systems biology; Uncertain kinetic rates

Indexed keywords

ABSTRACTING; BIOLOGICAL SYSTEMS; KINETICS; MARKOV PROCESSES; SEMANTICS;

ABSTRACT INTERPRETATIONS; INTERVAL MARKOV CHAINS; PROBABILISTIC MODEL CHECKING; SYSTEMS BIOLOGY; UNCERTAIN KINETIC RATES;

MODEL CHECKING;

EID: 84992268376     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-04420-5_8     Document Type: Conference Paper

References (32)

1. Cervesato, I., Durgin, N.A., Lincoln, P., Mitchell, J.C., Scedrov, A.: A metanotation for protocol analysis. In: CSFW, pp. 55–69 (1999)
2. Cousot, P., Cousot, R.: Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints. In: POPL, pp. 238–252. ACM Press, New York (1977)
3. Jonsson, B., Larsen, K.G.: Specification and refinement of probabilistic processes. In: LICS, pp. 266–277. IEEE, Los Alamitos (1991)
4. Kozine, I., Utkin, L.V.: Interval-valued finite markov chains. Reliable Computing 8(2), 97–113 (2002)
5. Fecher, H., Leucker, M., Wolf, V.: Don’t Know in probabilistic systems. In: Valmari, A. (ed.) SPIN 2006. LNCS, vol. 3925, pp. 71–88. Springer, Heidelberg (2006)
6. Villasana, M., Radunskaya, A.: A delay differential equation model for tumor growth. J. of Math. Biol. 47, 270–294 (2003)
7. Kwiatkowska, M.Z.: Model checking for probability and time: from theory to practice. In: LICS, pp. 351–360. IEEE, Los Alamitos (2003)
8. Kwiatkowska, M.Z., Norman, G., Parker, D.: Prism: Probabilistic symbolic model checker. In: Field, T., Harrison, P.G., Bradley, J., Harder, U. (eds.) TOOLS 2002. LNCS, vol. 2324, pp. 200–204. Springer, Heidelberg (2002)
9. Hansson, H., Jonsson, B.: A logic for reasoning about time and reliability. Formal Asp. Comput. 6(5), 512–535 (1994)
10. Kearfott, R.B.: Interval computations: Introduction, uses, and resources. In: Euromath Bulletin, vol. 2, pp. 95–112. European Mathematical Trust (1996)
11. Weichselberger, K.: The theory of interval-probability as a unifying concept for uncertainty. In: Cooman, G.D., Cozman, F.G., Moral, S., Walley, P. (eds.) ISIPTA, pp. 387–396 (1999)
12. Coletta, A., Gori, R., Levi, F., 2009, Approximating probabilistic behaviors of biological systems using abstract interpretation, Electronic Notes in Theoretical Computer Science, 229(1), 165–182
13. D’Argenio, P.R., Jeannet, B., Jensen, H.E., Larsen, K.G.: Reachability analysis of probabilistic systems by successive refinements. In: de Luca, L., Gilmore, S. (eds.) PROBMIV 2001, PAPM-PROBMIV 2001, and PAPM 2001. LNCS, vol. 2165, pp. 39–56. Springer, Heidelberg (2001)
14. Yen, H.-C.: A note on fine covers and iterable factors of vas languages. Inf. Process. Lett. 56(5), 237-243 (1995)
15. Yen, H.-C.: On the regularity of petri net languages. Inf. Comput. 124(2), 168-181 (1996)
16. Huth, M.: On finite-state approximants for probabilistic computation tree logic. Theor. Comput. Sci. 246, 113–134 (2005)
17. Sen, K., Viswanathan, M., Agha, G.: Model-checking markov chains in the presence of uncertainties. In: Hermanns, H., Palsberg, J. (eds.) TACAS 2006. LNCS, vol. 3920, pp. 394–410. Springer, Heidelberg (2006)
18. Škulj, D.: Finite Discrete Time Markov Chains with Interval Probabilities. In: Lawry, J., Miranda, E., Bugar´ın, A., Li, S., Gil, M.A., Grzegorzewski, P., Hryniewicz, O. (eds.) SMPS, pp. 299–306. Springer, Heidelberg (2006)
19. Blanc, J.P.C., Hertog, D.D.: On Markov Chains with Uncertain Data. CentER Discussion Paper Series 50, Tilburg Univ., Center for Economic Research (2008)
20. Danos, V., Feret, J., Fontana, W., Krivine, J.: Abstract interpretation of cellular signalling networks. In: Logozzo, F., Peled, D.A., Zuck, L.D. (eds.) VMCAI 2008. LNCS, vol. 4905, pp. 83–97. Springer, Heidelberg (2008)
21. Fages, F., Soliman, S.: Formal Cell Biology in Biocham. In: Bernardo, M., Degano, P., Zavattaro, G. (eds.) SFM 2008. LNCS, vol. 5016, pp. 54–80. Springer, Heidelberg (2008)
22. Monniaux, D.: Abstract interpretation of programs as Markov decision processes. In: Sci. Comput. Program, vol. 58, pp. 179–205. Springer, Heidelberg (2005)
23. Di Pierro, A., Wiklicky, H.: Concurrent constraint programming: towards probabilistic abstract interpretation. In: PPDP, pp. 127–138. ACM, New York (2000)
24. Wilkinson, S.J., Benson, N., Kell, D.B.: Proximate parameter tuning for biochemical networks with uncertain kinetic parameters. In: Mol. bioSys., vol. 4, pp. 74–97. RSC Publishing (2008)
25. Batt, G., Belta, C., Weiss, R.: Model Checking Genetic Regulatory Networks with Parameter Uncertainty. In: Bemporad, A., Bicchi, A., Buttazzo, G. (eds.) HSCC 2007. LNCS, vol. 4416, pp. 61–75. Springer, Heidelberg (2007)
26. Manca, V.: The Metabolic Algorithm for P Systems: Principles and Applications. Theor. Comput. Sci. 404, 142–155 (2008)
27. Donaldson, R., Gilbert, D.: A Model Checking Approach to the Parameter Estimation of Biochemical Pathways. In: Heiner, M., Uhrmacher, A.M. (eds.) CMSB 2008. LNCS (LNBI), vol. 5307, pp. 269–287. Springer, Heidelberg (2008)
28. Fages, F., Soliman, S.: Model Revision from Temporal Logic Properties in Systems Biology. In: De Raedt, L., Frasconi, P., Kersting, K., Muggleton, S.H. (eds.) Probabilistic Inductive Logic Programming. LNCS, vol. 4911, pp. 287–304. Springer, Heidelberg (2008)
29. Lanotte, R., Maggiolo-Schettini, A., Troina, A.: Parametric probabilistic transition systems for system design and analysis. Form. Asp. Comput. 19, 93–109 (2007)
30. Han, T., Katoen, J.P., Mereacre, A.: Approximate Parameter Synthesis for Probabilistic Time-Bounded Reachability. In: RTSS, pp. 173–182. IEEE, Los Alamitos (2008)
31. Katoen, J.P., Klink, D., Leucker, M., Wolf, V.: Three-Valued Abstraction for Continuous-Time Markov Chains. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 311–324. Springer, Heidelberg (2007)
32. Baier, C., Hermanns, H., Katoen, J.P., Haverkort, B.R.: Efficient computation of time-bounded reachability probabilities in uniform continuous-time Markov decision processes. Theor. Comput. Sci. 345, 2–26 (2005)