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2017 | OriginalPaper | Chapter

Pithya: A Parallel Tool for Parameter Synthesis of Piecewise Multi-affine Dynamical Systems

Authors : Nikola Beneš, Luboš Brim, Martin Demko, Samuel Pastva, David Šafránek

Published in: Computer Aided Verification

Publisher: Springer International Publishing

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Abstract

We present a novel tool for parameter synthesis of piecewise multi-affine dynamical systems from specifications expressed in a hybrid branching-time temporal logic. The tool is based on the algorithm of parallel semi-symbolic coloured model checking that extends standard model checking methods to cope with parametrised Kripke structures. The tool implements state-of-the-art techniques developed in our previous research and is primarily intended to be used for the analysis of dynamical systems with uncertain parameters that frequently arise in computational systems biology. However, it can be employed for any dynamical system where the non-linear equations can be sufficiently well approximated by piecewise multi-affine equations.

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Literature
2.
go back to reference Arellano, G., Argil, J., Azpeitia, E., Benítez, M., Carrillo, M., Góngora, P., Rosenblueth, D.A., Alvarez-Buylla, E.R.: “Antelope”: a hybrid-logic model checker for branching-time Boolean GRN analysis. BMC Bioinf. 12(1), 1–15 (2011)CrossRef Arellano, G., Argil, J., Azpeitia, E., Benítez, M., Carrillo, M., Góngora, P., Rosenblueth, D.A., Alvarez-Buylla, E.R.: “Antelope”: a hybrid-logic model checker for branching-time Boolean GRN analysis. BMC Bioinf. 12(1), 1–15 (2011)CrossRef
3.
go back to reference Batt, G., Page, M., Cantone, I., Gössler, G., Monteiro, P., de Jong, H.: Efficient parameter search for qualitative models of regulatory networks using symbolic model checking. Bioinformatics 26(18), 603–610 (2010)CrossRef Batt, G., Page, M., Cantone, I., Gössler, G., Monteiro, P., de Jong, H.: Efficient parameter search for qualitative models of regulatory networks using symbolic model checking. Bioinformatics 26(18), 603–610 (2010)CrossRef
4.
go back to reference Batt, G., Yordanov, B., Weiss, R., Belta, C.: Robustness analysis and tuning of synthetic gene networks. Bioinformatics 23(18), 2415–2422 (2007)CrossRef Batt, G., Yordanov, B., Weiss, R., Belta, C.: Robustness analysis and tuning of synthetic gene networks. Bioinformatics 23(18), 2415–2422 (2007)CrossRef
5.
go back to reference ter Beek, M.H., Fantechi, A., Gnesi, S., Mazzanti, F.: A state/event-based model-checking approach for the analysis of abstract system properties. Sci. Comput. Program. 76(2), 119–135 (2011)CrossRefMATH ter Beek, M.H., Fantechi, A., Gnesi, S., Mazzanti, F.: A state/event-based model-checking approach for the analysis of abstract system properties. Sci. Comput. Program. 76(2), 119–135 (2011)CrossRefMATH
6.
go back to reference Beneš, N., Brim, L., Demko, M., Pastva, S., Šafránek, D.: Parallel SMT-based parameter synthesis with application to piecewise multi-affine systems. In: ATVA 2016. LNCS, vol. 9936, pp. 1–17. Springer, Cham (2016) Beneš, N., Brim, L., Demko, M., Pastva, S., Šafránek, D.: Parallel SMT-based parameter synthesis with application to piecewise multi-affine systems. In: ATVA 2016. LNCS, vol. 9936, pp. 1–17. Springer, Cham (2016)
7.
go back to reference Beneš, N., Brim, L., Demko, M., Pastva, S., Šafránek, D.: A model checking approach to discrete bifurcation analysis. In: Fitzgerald, J., Heitmeyer, C., Gnesi, S., Philippou, A. (eds.) FM 2016. LNCS, vol. 9995, pp. 85–101. Springer, Cham (2016). doi:10.1007/978-3-319-48989-6_6 Beneš, N., Brim, L., Demko, M., Pastva, S., Šafránek, D.: A model checking approach to discrete bifurcation analysis. In: Fitzgerald, J., Heitmeyer, C., Gnesi, S., Philippou, A. (eds.) FM 2016. LNCS, vol. 9995, pp. 85–101. Springer, Cham (2016). doi:10.​1007/​978-3-319-48989-6_​6
8.
go back to reference Bengtsson, J., Larsen, K., Larsson, F., Pettersson, P., Yi, W.: UPPAAL — a tool suite for automatic verification of real-time systems. In: Alur, R., Henzinger, T.A., Sontag, E.D. (eds.) HS 1995. LNCS, vol. 1066, pp. 232–243. Springer, Heidelberg (1996). doi:10.1007/BFb0020949 CrossRef Bengtsson, J., Larsen, K., Larsson, F., Pettersson, P., Yi, W.: UPPAAL — a tool suite for automatic verification of real-time systems. In: Alur, R., Henzinger, T.A., Sontag, E.D. (eds.) HS 1995. LNCS, vol. 1066, pp. 232–243. Springer, Heidelberg (1996). doi:10.​1007/​BFb0020949 CrossRef
9.
go back to reference Bogomolov, S., Schilling, C., Bartocci, E., Batt, G., Kong, H., Grosu, R.: Abstraction-based parameter synthesis for multiaffine systems. In: Piterman, N. (ed.) HVC 2015. LNCS, vol. 9434, pp. 19–35. Springer, Cham (2015). doi:10.1007/978-3-319-26287-1_2 CrossRef Bogomolov, S., Schilling, C., Bartocci, E., Batt, G., Kong, H., Grosu, R.: Abstraction-based parameter synthesis for multiaffine systems. In: Piterman, N. (ed.) HVC 2015. LNCS, vol. 9434, pp. 19–35. Springer, Cham (2015). doi:10.​1007/​978-3-319-26287-1_​2 CrossRef
10.
go back to reference Bortolussi, L., Milios, D., Sanguinetti, G.: U-check: model checking and parameter synthesis under uncertainty. In: Campos, J., Haverkort, B.R. (eds.) QEST 2015. LNCS, vol. 9259, pp. 89–104. Springer, Cham (2015). doi:10.1007/978-3-319-22264-6_6 CrossRef Bortolussi, L., Milios, D., Sanguinetti, G.: U-check: model checking and parameter synthesis under uncertainty. In: Campos, J., Haverkort, B.R. (eds.) QEST 2015. LNCS, vol. 9259, pp. 89–104. Springer, Cham (2015). doi:10.​1007/​978-3-319-22264-6_​6 CrossRef
11.
go back to reference Brim, L., Češka, M., Demko, M., Pastva, S., Šafránek, D.: Parameter synthesis by parallel coloured CTL model checking. In: Roux, O., Bourdon, J. (eds.) CMSB 2015. LNCS, vol. 9308, pp. 251–263. Springer, Cham (2015). doi:10.1007/978-3-319-23401-4_21 CrossRef Brim, L., Češka, M., Demko, M., Pastva, S., Šafránek, D.: Parameter synthesis by parallel coloured CTL model checking. In: Roux, O., Bourdon, J. (eds.) CMSB 2015. LNCS, vol. 9308, pp. 251–263. Springer, Cham (2015). doi:10.​1007/​978-3-319-23401-4_​21 CrossRef
12.
go back to reference Brim, L., Demko, M., Pastva, S., Šafránek, D.: High-performance discrete bifurcation analysis for piecewise-affine dynamical systems. In: Abate, A., Šafránek, D. (eds.) HSB 2015. LNCS, vol. 9271, pp. 58–74. Springer, Cham (2015). doi:10.1007/978-3-319-26916-0_4 CrossRef Brim, L., Demko, M., Pastva, S., Šafránek, D.: High-performance discrete bifurcation analysis for piecewise-affine dynamical systems. In: Abate, A., Šafránek, D. (eds.) HSB 2015. LNCS, vol. 9271, pp. 58–74. Springer, Cham (2015). doi:10.​1007/​978-3-319-26916-0_​4 CrossRef
13.
go back to reference Brim, L., Vejpustek, T., Šafránek, D., Fabriková, J.: Robustness analysis for value-freezing signal temporal logic. In: HSB 2013, EPTCS, vol. 125, pp. 20–36 (2013) Brim, L., Vejpustek, T., Šafránek, D., Fabriková, J.: Robustness analysis for value-freezing signal temporal logic. In: HSB 2013, EPTCS, vol. 125, pp. 20–36 (2013)
14.
go back to reference Brim, L., Yorav, K., Žídková, J.: Assumption-based distribution of CTL model checking. STTT 7(1), 61–73 (2005)CrossRef Brim, L., Yorav, K., Žídková, J.: Assumption-based distribution of CTL model checking. STTT 7(1), 61–73 (2005)CrossRef
15.
go back to reference Češka, M., Pilař, P., Paoletti, N., Brim, L., Kwiatkowska, M.: PRISM-PSY: precise GPU-accelerated parameter synthesis for stochastic systems. In: Chechik, M., Raskin, J.-F. (eds.) TACAS 2016. LNCS, vol. 9636, pp. 367–384. Springer, Heidelberg (2016). doi:10.1007/978-3-662-49674-9_21 CrossRef Češka, M., Pilař, P., Paoletti, N., Brim, L., Kwiatkowska, M.: PRISM-PSY: precise GPU-accelerated parameter synthesis for stochastic systems. In: Chechik, M., Raskin, J.-F. (eds.) TACAS 2016. LNCS, vol. 9636, pp. 367–384. Springer, Heidelberg (2016). doi:10.​1007/​978-3-662-49674-9_​21 CrossRef
16.
go back to reference Clarke, E.M., Emerson, E.A., Sistla, A.P.: Automatic verification of finite-state concurrent systems using temporal logic specifications. ACM Trans. Program. Lang. Syst. 8(2), 244–263 (1986)CrossRefMATH Clarke, E.M., Emerson, E.A., Sistla, A.P.: Automatic verification of finite-state concurrent systems using temporal logic specifications. ACM Trans. Program. Lang. Syst. 8(2), 244–263 (1986)CrossRefMATH
17.
go back to reference Dehnert, C., Junges, S., Jansen, N., Corzilius, F., Volk, M., Bruintjes, H., Katoen, J.-P., Ábrahám, E.: PROPhESY: a probabilistic parameter synthesis tool. In: Kroening, D., Păsăreanu, C.S. (eds.) CAV 2015. LNCS, vol. 9206, pp. 214–231. Springer, Cham (2015). doi:10.1007/978-3-319-21690-4_13 CrossRef Dehnert, C., Junges, S., Jansen, N., Corzilius, F., Volk, M., Bruintjes, H., Katoen, J.-P., Ábrahám, E.: PROPhESY: a probabilistic parameter synthesis tool. In: Kroening, D., Păsăreanu, C.S. (eds.) CAV 2015. LNCS, vol. 9206, pp. 214–231. Springer, Cham (2015). doi:10.​1007/​978-3-319-21690-4_​13 CrossRef
18.
go back to reference Demko, M., Beneš, N., Brim, L., Pastva, S., Šafránek, D.: High-performance symbolic parameter synthesis of biological models: a case study. In: Bartocci, E., Lio, P., Paoletti, N. (eds.) CMSB 2016. LNCS, vol. 9859, pp. 82–97. Springer, Cham (2016). doi:10.1007/978-3-319-45177-0_6 CrossRef Demko, M., Beneš, N., Brim, L., Pastva, S., Šafránek, D.: High-performance symbolic parameter synthesis of biological models: a case study. In: Bartocci, E., Lio, P., Paoletti, N. (eds.) CMSB 2016. LNCS, vol. 9859, pp. 82–97. Springer, Cham (2016). doi:10.​1007/​978-3-319-45177-0_​6 CrossRef
19.
go back to reference Donzé, A., Fanchon, E., Gattepaille, L.M., Maler, O., Tracqui, P.: Robustness analysis and behavior discrimination in enzymatic reaction networks. PLoS ONE 6(9), e24246 (2011)CrossRef Donzé, A., Fanchon, E., Gattepaille, L.M., Maler, O., Tracqui, P.: Robustness analysis and behavior discrimination in enzymatic reaction networks. PLoS ONE 6(9), e24246 (2011)CrossRef
20.
go back to reference Dreossi, T.: Sapo: Reachability computation and parameter synthesis of polynomial dynamical systems. CoRR abs/1607.02200 (2016) Dreossi, T.: Sapo: Reachability computation and parameter synthesis of polynomial dynamical systems. CoRR abs/1607.02200 (2016)
21.
go back to reference Fisher, J., Henzinger, T.: Executable cell biology. Nat. Biotechnol. 25(11), 1239–1249 (2007)CrossRef Fisher, J., Henzinger, T.: Executable cell biology. Nat. Biotechnol. 25(11), 1239–1249 (2007)CrossRef
22.
go back to reference Grosu, R., Batt, G., Fenton, F.H., Glimm, J., Guernic, C., Smolka, S.A., Bartocci, E.: From cardiac cells to genetic regulatory networks. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 396–411. Springer, Heidelberg (2011). doi:10.1007/978-3-642-22110-1_31 CrossRef Grosu, R., Batt, G., Fenton, F.H., Glimm, J., Guernic, C., Smolka, S.A., Bartocci, E.: From cardiac cells to genetic regulatory networks. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 396–411. Springer, Heidelberg (2011). doi:10.​1007/​978-3-642-22110-1_​31 CrossRef
23.
go back to reference Hajnal, M., Šafránek, D., Demko, M., Pastva, S., Krejčí, P., Brim, L.: Toward modelling and analysis of transient and sustained behaviour of signalling pathways. In: Cinquemani, E., Donzé, A. (eds.) HSB 2016. LNCS, vol. 9957, pp. 57–66. Springer, Cham (2016). doi:10.1007/978-3-319-47151-8_4 Hajnal, M., Šafránek, D., Demko, M., Pastva, S., Krejčí, P., Brim, L.: Toward modelling and analysis of transient and sustained behaviour of signalling pathways. In: Cinquemani, E., Donzé, A. (eds.) HSB 2016. LNCS, vol. 9957, pp. 57–66. Springer, Cham (2016). doi:10.​1007/​978-3-319-47151-8_​4
24.
go back to reference Madsen, C., Shmarov, F., Zuliani, P.: BioPSy: an SMT-based tool for guaranteed parameter set synthesis of biological models. In: Roux, O., Bourdon, J. (eds.) CMSB 2015. LNCS, vol. 9308, pp. 182–194. Springer, Cham (2015). doi:10.1007/978-3-319-23401-4_16 CrossRef Madsen, C., Shmarov, F., Zuliani, P.: BioPSy: an SMT-based tool for guaranteed parameter set synthesis of biological models. In: Roux, O., Bourdon, J. (eds.) CMSB 2015. LNCS, vol. 9308, pp. 182–194. Springer, Cham (2015). doi:10.​1007/​978-3-319-23401-4_​16 CrossRef
26.
go back to reference Rizk, A., Batt, G., Fages, F., Soliman, S.: A general computational method for robustness analysis with applications to synthetic gene networks. Bioinformatics 25(12), i169–i178 (2009)CrossRef Rizk, A., Batt, G., Fages, F., Soliman, S.: A general computational method for robustness analysis with applications to synthetic gene networks. Bioinformatics 25(12), i169–i178 (2009)CrossRef
27.
go back to reference Schivo, S., Scholma, J., van der Vet, P.E., Karperien, M., Post, J.N., van de Pol, J., Langerak, R.: Modelling with animo: between fuzzy logic and differential equations. BMC Syst. Biol. 10(1), 56 (2016)CrossRef Schivo, S., Scholma, J., van der Vet, P.E., Karperien, M., Post, J.N., van de Pol, J., Langerak, R.: Modelling with animo: between fuzzy logic and differential equations. BMC Syst. Biol. 10(1), 56 (2016)CrossRef
28.
go back to reference Streck, A.: Toolkit for reverse engineering of molecular pathways via parameter identification. Ph.D. thesis, Free University of Berlin, Germany (2016) Streck, A.: Toolkit for reverse engineering of molecular pathways via parameter identification. Ph.D. thesis, Free University of Berlin, Germany (2016)
29.
go back to reference Streck, A., Kolčák, J., Siebert, H., Šafránek, D.: Esther: introducing an online platform for parameter identification of boolean networks. In: Gupta, A., Henzinger, T.A. (eds.) CMSB 2013. LNBI, vol. 8130, pp. 257–258. Springer, Heidelberg (2013) Streck, A., Kolčák, J., Siebert, H., Šafránek, D.: Esther: introducing an online platform for parameter identification of boolean networks. In: Gupta, A., Henzinger, T.A. (eds.) CMSB 2013. LNBI, vol. 8130, pp. 257–258. Springer, Heidelberg (2013)
Metadata
Title
Pithya: A Parallel Tool for Parameter Synthesis of Piecewise Multi-affine Dynamical Systems
Authors
Nikola Beneš
Luboš Brim
Martin Demko
Samuel Pastva
David Šafránek
Copyright Year
2017
DOI
https://doi.org/10.1007/978-3-319-63387-9_29

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