Abstract
This paper presents an Interval Decision Diagram based approach to symbolic CSL model checking of Continuous Time Markov Chains which are derived from stochastic Petri nets. Matrix-vector and vector-matrix multiplication are the major tasks of exact analysis. We introduce a simple, but powerful algorithm which uses explicitly the Petri net structure and allows for parallelisation. We present results demonstrating the efficiency of our first prototype implementation when applied to biochemical network models, specifically with increasing token numbers. Our tool currently supports CSL model checking of time-bounded operators and the Next operator for ordinary stochastic Petri nets.
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References
Aziz, A., Sanwal, K., Singhal, V., Brayton, R.: Model checking continuous time Markov chains. ACM Trans. on Computational Logic 1(1) (2000)
Baier, C., Haverkort, B., Hermanns, H., Katoen, J.-P.: Model checking Contiuous-Time Markov Chains by transient Analysis. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 358–372. Springer, Heidelberg (2000)
Barkai, N., Leibler, S.: Biological rhythms: Circadian clocks limited by noise. Nature 403, 267–268 (2000)
Cerotti, D., D’Aprile, D., Donatelli, S., Sproston, J.: Verifying stochastic well-formed nets with CSL model checking tools. In: Proc. ACSD 2006, pp. 143–152. IEEE Computer Society, Los Alamitos (2006)
Ciardo, G., Jones III, R.L., Miner, A.S., Siminiceanu, R.I.: Logic and stochastic modeling with smart. Perform. Eval. 63(6), 578–608 (2006)
Cho, K.-H., Shin, S.-Y., Kim, H.-W., Wolkenhauer, O., McFerran, B., Kolch, W.: Mathematical modeling of the influence of RKIP on the ERK signaling pathway. In: Priami, C. (ed.) CMSB 2003. LNCS, vol. 2602, pp. 127–141. Springer, Heidelberg (2003)
Calder, M., Vyshemirsky, V., Orton, R., Gilbert, D.: Analysis of Signalling Pathways using the PRISM model checker. In: Proc. CMSB 2005, pp. 179–190. LFCS, Univ. of Edinburgh (2005)
Gilbert, D., Heiner, M.: From Petri nets to differential equations - an integrative approach for biochemical network analysis. In: Donatelli, S., Thiagarajan, P.S. (eds.) ICATPN 2006. LNCS, vol. 4024, pp. 181–200. Springer, Heidelberg (2006)
Gilbert, D., Heiner, M., Lehrack, S.: A unifying framework for modelling and analysing biochemical pathways using Petri nets. In: Calder, M., Gilmore, S. (eds.) CMSB 2007. LNCS (LNBI), vol. 4695, pp. 200–216. Springer, Heidelberg (2007)
Heiner, M., Donaldson, R., Gilbert, D.: Petri Nets for Systems Biology. In: Iyengar, M.S. (ed.) Symbolic Systems Biology: Theory and Methods, Jones and Bartlett Publishers, Inc. (in press, 2010)
Heiner, M., Gilbert, D., Donaldson, R.: Petri nets for systems and synthetic biology. In: Bernardo, M., Degano, P., Zavattaro, G. (eds.) SFM 2008. LNCS, vol. 5016, pp. 215–264. Springer, Heidelberg (2008)
Heiner, M., Richter, R., Schwarick, M.: Snoopy - a tool to design and animate/simulate graph-based formalisms. In: Proc. PNTAP 2008, associated to SIMUTools 2008. ACM digital library, New York (2008)
Heiner, M., Schwarick, M., Tovchigrechko, A.: DSSZ-MC - A Tool for Symbolic Analysis of Extended Petri Nets. In: Franceschinis, G., Wolf, K. (eds.) Petri Nets 2009. LNCS, vol. 5606, pp. 323–332. Springer, Heidelberg (2009)
Jansen, D.N., Katoen, J.-P., Oldenkamp, M., Stoelinga, M., Zapreev, I.: How fast and fat is your probabilistic model checker? In: Yorav, K. (ed.) HVC 2007. LNCS, vol. 4899, pp. 69–85. Springer, Heidelberg (2008)
Kwiatkowska, M., Norman, G., Parker, D.: Using probabilistic model checking in systems biology. ACM SIGMETRICS Performance Evaluation Review 35(4), 14–21 (2008)
Levchenko, A., Bruck, J., Sternberg, P.W.: Scaffold proteins may biphasically affect the levels of mitogen-activated protein kinase signaling and reduce its threshold properties. Proc. Natl. Acad. Sci. USA 97(11), 5818–5823 (2000)
Miner, A.S., Ciardo, G.: Efficient Reachability Set Generation and Storage Using Decision Diagrams. In: Donatelli, S., Kleijn, J. (eds.) ICATPN 1999. LNCS, vol. 1639, pp. 6–25. Springer, Heidelberg (1999)
Noack, A.: A ZBDD Package for Efficient Model Checking of Petri Nets (in German). Technical report, BTU Cottbus, Dep. of CS (1999)
Parker, D.: Implementation of Symbolic Model Checking for Probabilistic Systems. PhD thesis, University of Birmingham (2002)
Peccoud, J., Courtney, T., Sanders, W.H.: Möbius: an integrated discrete-event modeling environment. Bioinformatics 23(24), 3412–3414 (2007)
Parker, D., Norman, G., Kwiatkowska, M.: PRISM 3.0.beta1 Users’ Guide (2006)
Snoopy Website. A Tool to Design and Animate/Simulate Graphs. BTU Cottbus (2008), http://www-dssz.informatik.tu-cottbus.de/software/snoopy.html
Stewart, W.J.: Introduction to the Numerical Solution of Markov Chains. Princeton Univ. Press, Princeton (1994)
Tovchigrechko, A.: Model Checking Using Interval Decision Diagrams. PhD thesis, BTU Cottbus, Dep. of CS (2008)
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Schwarick, M., Heiner, M. (2009). CSL Model Checking of Biochemical Networks with Interval Decision Diagrams. In: Degano, P., Gorrieri, R. (eds) Computational Methods in Systems Biology. CMSB 2009. Lecture Notes in Computer Science(), vol 5688. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03845-7_20
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DOI: https://doi.org/10.1007/978-3-642-03845-7_20
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