Skip to main content

2021 | OriginalPaper | Buchkapitel

A Design of GPU-Based Quantitative Model Checking

verfasst von : YoungMin Kwon, Eunhee Kim

Erschienen in: Verification, Model Checking, and Abstract Interpretation

Verlag: Springer International Publishing

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

In this paper, we implement a GPU-based quantitative model checker and compare its performance with a CPU-based one. Linear Temporal Logic for Control (LTLC) is a quantitative variation of LTL to describe properties of a linear system and LTLC-Checker [1] is an implementation of its model checking algorithm. In practice, its long and unpredictable execution time has been a concern in applying the technique to real-time applications such as automatic control systems. In this paper, we design an LTLC model checker using a GPGPU programming technique. The resulting model checker is not only faster than the CPU-based one especially when the problem is not simple, but it has less variation in the execution time as well. Furthermore, multiple counterexamples can be found together when the CPU-based checker can find only one.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Fußnoten
1
To distinguish with other queues, we call the queue for the BFS a BFS queue or a BFS-Q.
 
2
The terms beginning with capital letters like Task and DevTask represent types and those beginning with small letters like task and devTask represent their instances.
 
Literatur
2.
Zurück zum Zitat Ahamed, A.K.C., Magoulès, F.: Parallel sub-structuring methods for solving sparse linear systems on a cluster of GPUs. In: 2014 IEEE International Conference on High Performance Computing and Communications, 2014 IEEE 6th International Symposium on Cyberspace Safety and Security, 2014 IEEE 11th International Conference on Embedded Software and System (HPCC, CSS, ICESS), pp. 121–128. IEEE (2014) Ahamed, A.K.C., Magoulès, F.: Parallel sub-structuring methods for solving sparse linear systems on a cluster of GPUs. In: 2014 IEEE International Conference on High Performance Computing and Communications, 2014 IEEE 6th International Symposium on Cyberspace Safety and Security, 2014 IEEE 11th International Conference on Embedded Software and System (HPCC, CSS, ICESS), pp. 121–128. IEEE (2014)
3.
Zurück zum Zitat Ahamed, A.K.C., Magoulès, F.: GPU accelerated substructuring methods for sparse linear systems. In: 2016 IEEE International Conference on Computational Science and Engineering (CSE) and IEEE International Conference on Embedded and Ubiquitous Computing (EUC) and 15th International Symposium on Distributed Computing and Applications for Business Engineering (DCABES), pp. 614–625. IEEE (2016) Ahamed, A.K.C., Magoulès, F.: GPU accelerated substructuring methods for sparse linear systems. In: 2016 IEEE International Conference on Computational Science and Engineering (CSE) and IEEE International Conference on Embedded and Ubiquitous Computing (EUC) and 15th International Symposium on Distributed Computing and Applications for Business Engineering (DCABES), pp. 614–625. IEEE (2016)
6.
Zurück zum Zitat Barnat, J., Bauch, P., Brim, L., Ceska, M.: Employing multiple CUDA devices to accelerate LTL model checking. In: 2010 IEEE 16th International Conference on Parallel and Distributed Systems, pp. 259–266. IEEE (2010) Barnat, J., Bauch, P., Brim, L., Ceska, M.: Employing multiple CUDA devices to accelerate LTL model checking. In: 2010 IEEE 16th International Conference on Parallel and Distributed Systems, pp. 259–266. IEEE (2010)
7.
Zurück zum Zitat Bartocci, E., DeFrancisco, R., Smolka, S.A.: Towards a GPGPU-parallel SPIN model checker. In: International SPIN Symposium on Model Checking of Software, pp. 87–96. ACM (2014) Bartocci, E., DeFrancisco, R., Smolka, S.A.: Towards a GPGPU-parallel SPIN model checker. In: International SPIN Symposium on Model Checking of Software, pp. 87–96. ACM (2014)
8.
Zurück zum Zitat Bu, L., Li, Y., Wang, L., Li, X.: BACH: bounded reachability checker for linear hybrid automata. In: Formal Methods in Computer Aided Design, pp. 65–68. IEEE Computer Society (2008) Bu, L., Li, Y., Wang, L., Li, X.: BACH: bounded reachability checker for linear hybrid automata. In: Formal Methods in Computer Aided Design, pp. 65–68. IEEE Computer Society (2008)
9.
Zurück zum Zitat Büchi, J.: On a decision method in restricted second order arithmetic. In: Proceedings of the International Conference on Logic, Methodology and Philosophy of Science, pp. 1–11. Stanford University Press (1960) Büchi, J.: On a decision method in restricted second order arithmetic. In: Proceedings of the International Conference on Logic, Methodology and Philosophy of Science, pp. 1–11. Stanford University Press (1960)
10.
Zurück zum Zitat Clarke, D., Mohtai, C., Tuffs, P.: Generalized predictive control. Automatica 23, 137–160 (1987)CrossRef Clarke, D., Mohtai, C., Tuffs, P.: Generalized predictive control. Automatica 23, 137–160 (1987)CrossRef
11.
Zurück zum Zitat Clarke, D., Scattolini, R.: Constrained receding-horizon predictive control. In: IEE Proceedings Part D, vol. 138, pp. 347–354 (1991) Clarke, D., Scattolini, R.: Constrained receding-horizon predictive control. In: IEE Proceedings Part D, vol. 138, pp. 347–354 (1991)
12.
Zurück zum Zitat Clarke, E., Grumberg, O., Peled, D.: Model Checking. MIT Press, Cambridge (2000)MATH Clarke, E., Grumberg, O., Peled, D.: Model Checking. MIT Press, Cambridge (2000)MATH
13.
Zurück zum Zitat Franklin, G.F., Powell, J.D., Emami-Naeini, A.: Feedback control of dynamic systems, vol. 3 (2002) Franklin, G.F., Powell, J.D., Emami-Naeini, A.: Feedback control of dynamic systems, vol. 3 (2002)
14.
Zurück zum Zitat Fränzle, M., Herde, C.: HySAT: an efficient proof engine for bounded model checking of hybrid systems. Formal Methods Syst. Des. 30, 179–198 (2007)CrossRef Fränzle, M., Herde, C.: HySAT: an efficient proof engine for bounded model checking of hybrid systems. Formal Methods Syst. Des. 30, 179–198 (2007)CrossRef
15.
Zurück zum Zitat Girard, A., Pola, G., Tabuada, P.: Approximately bisimilar symbolic models for incrementally stable switched systems. Trans. Autom. Control 55, 116–126 (2010)MathSciNetCrossRef Girard, A., Pola, G., Tabuada, P.: Approximately bisimilar symbolic models for incrementally stable switched systems. Trans. Autom. Control 55, 116–126 (2010)MathSciNetCrossRef
16.
Zurück zum Zitat Henzinger, T.A.: The theory of hybrid automata. In: Annual Symposium on Logic in Computer Science, pp. 278–292. IEEE Computer Society (1996) Henzinger, T.A.: The theory of hybrid automata. In: Annual Symposium on Logic in Computer Science, pp. 278–292. IEEE Computer Society (1996)
18.
Zurück zum Zitat Holzmann, G.J.: The model checker SPIN. IEEE Trans. Softw. Eng. 23, 279–295 (1997)CrossRef Holzmann, G.J.: The model checker SPIN. IEEE Trans. Softw. Eng. 23, 279–295 (1997)CrossRef
20.
Zurück zum Zitat Karmarkar, N.: A new polynomial-time algorithm for linear programming. In: Combinatorica, vol. 4, pp. 373–395 (1984) Karmarkar, N.: A new polynomial-time algorithm for linear programming. In: Combinatorica, vol. 4, pp. 373–395 (1984)
21.
Zurück zum Zitat Khun, J., Šimeček, I., Lórencz, R.: GPU solver for systems of linear equations with infinite precision. In: 2015 17th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC), pp. 121–124. IEEE (2015) Khun, J., Šimeček, I., Lórencz, R.: GPU solver for systems of linear equations with infinite precision. In: 2015 17th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC), pp. 121–124. IEEE (2015)
22.
Zurück zum Zitat Kloetzer, M., Belta, C.: A fully automated framework for control of linear systems from temporal logic specifications. Trans. Autom. Control 53, 287–297 (2008)MathSciNetCrossRef Kloetzer, M., Belta, C.: A fully automated framework for control of linear systems from temporal logic specifications. Trans. Autom. Control 53, 287–297 (2008)MathSciNetCrossRef
24.
Zurück zum Zitat Kwon, Y., Kim, E.: Bounded model checking of hybrid systems for control. IEEE Trans. Autom. Control 60, 2961–2976 (2015)MathSciNetCrossRef Kwon, Y., Kim, E.: Bounded model checking of hybrid systems for control. IEEE Trans. Autom. Control 60, 2961–2976 (2015)MathSciNetCrossRef
25.
Zurück zum Zitat Larsen, K.G., Pettersson, P., Yi, W.: UPPAAL in a nutshell. Int. J. Softw. Tools Technol. Transf. 1, 134–152 (1997)CrossRef Larsen, K.G., Pettersson, P., Yi, W.: UPPAAL in a nutshell. Int. J. Softw. Tools Technol. Transf. 1, 134–152 (1997)CrossRef
26.
Zurück zum Zitat Law, A.M., Kelton, W.D.: Simulation Modeling & Analysis. McGraw-Hill, New York (1991)MATH Law, A.M., Kelton, W.D.: Simulation Modeling & Analysis. McGraw-Hill, New York (1991)MATH
27.
Zurück zum Zitat Lichtenstein, O., Pnueli, A.: Checking that finite state concurrent programs satisfy their linear specification. In: POPL, pp. 97–107 (1985) Lichtenstein, O., Pnueli, A.: Checking that finite state concurrent programs satisfy their linear specification. In: POPL, pp. 97–107 (1985)
28.
Zurück zum Zitat Liu, J., Ozay, N., Topcu, U., Murray, R.M.: Synthesis of reactive switching protocols from temporal logic specifications. Trans. Autom. Control 58(7), 1771–1785 (2013)MathSciNetCrossRef Liu, J., Ozay, N., Topcu, U., Murray, R.M.: Synthesis of reactive switching protocols from temporal logic specifications. Trans. Autom. Control 58(7), 1771–1785 (2013)MathSciNetCrossRef
29.
Zurück zum Zitat Luenberger, D.G.: Linear and Nonlinear Programming, 2nd edn. Addison Wesley, Boston (1989)MATH Luenberger, D.G.: Linear and Nonlinear Programming, 2nd edn. Addison Wesley, Boston (1989)MATH
30.
Zurück zum Zitat McClanahan, C.: History and evolution of GPU architecture. A Survey Paper, p. 9 (2010) McClanahan, C.: History and evolution of GPU architecture. A Survey Paper, p. 9 (2010)
31.
Zurück zum Zitat Miné, A.: The octagon abstract domain. In: Proceedings Eighth Working Conference on Reverse Engineering, pp. 310–319. IEEE (2001) Miné, A.: The octagon abstract domain. In: Proceedings Eighth Working Conference on Reverse Engineering, pp. 310–319. IEEE (2001)
32.
Zurück zum Zitat Ramanathan, R.: Intel multi-core processors: making the move to quad-core and beyond. Technology@ Intel Mag. 4(9), 2–4 (2006) Ramanathan, R.: Intel multi-core processors: making the move to quad-core and beyond. Technology@ Intel Mag. 4(9), 2–4 (2006)
Metadaten
Titel
A Design of GPU-Based Quantitative Model Checking
verfasst von
YoungMin Kwon
Eunhee Kim
Copyright-Jahr
2021
DOI
https://doi.org/10.1007/978-3-030-67067-2_20