Multi-core SCC-Based LTL Model Checking

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10028)

Abstract

We investigate and improve the scalability of multi-core LTL model checking. Our algorithm, based on parallel DFS-like SCC decomposition, is able to efficiently decompose large SCCs on-the-fly, which is a difficult problem to solve in parallel.

To validate the algorithm we performed experiments on a 64-core machine. We used an extensive set of well-known benchmark collections obtained from the BEEM database and the Model Checking Contest. We show that the algorithm is competitive with the current state-of-the-art model checking algorithms. For larger models we observe that our algorithm outperforms the competitors. We investigate how graph characteristics relate to and pose limitations on the achieved speedups.

References

  1. 1.
    Blahoudek, F., Duret-Lutz, A., Křetínský, M., Strejček, J.: Is there a best Büchi automaton for explicit model checking? In: Proceedings of the 2014 International SPIN Symposium on Model Checking of Software, SPIN 2014, pp. 68–76. ACM (2014)Google Scholar
  2. 2.
    Bloemen, V., Laarman, A., van de Pol, J.: Multi-core on-the-fly SCC decomposition. In: Proceedings of the 21st ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming, PPoPP 2016, pp. 8:1–8:12. ACM (2016)Google Scholar
  3. 3.
    Courcoubetis, C., Vardi, M., Wolper, P., Yannakakis, M.: Memory-efficient algorithms for the verification of temporal properties. In: Kurshan, R. (ed.) Computer-Aided Verification, pp. 129–142. Springer US, New York (1993)CrossRefGoogle Scholar
  4. 4.
    Couvreur, J.-M.: On-the-fly verification of linear temporal logic. In: Wing, J.M., Woodcock, J., Davies, J. (eds.) FM 1999. LNCS, vol. 1708, pp. 253–271. Springer, Heidelberg (1999). doi:10.1007/3-540-48119-2_16 Google Scholar
  5. 5.
    Couvreur, J.-M., Duret-Lutz, A., Poitrenaud, D.: On-the-fly emptiness checks for generalized Büchi automata. In: Godefroid, P. (ed.) SPIN 2005. LNCS, vol. 3639, pp. 169–184. Springer, Heidelberg (2005). doi:10.1007/11537328_15 CrossRefGoogle Scholar
  6. 6.
    Dijkstra, E.W.: Finding the maximum strong components in a directed graph. In: Dijkstra, E.W. (ed.) Selected Writings on Computing: A personal Perspective. Texts and Monographs in Computer Science, pp. 22–30. Springer, New York (1982)CrossRefGoogle Scholar
  7. 7.
    Duret-Lutz, A., Lewkowicz, A., Fauchille, A., Michaud, T., Renault, É., Xu, L.: Spot 2.0 — a framework for LTL and \(\omega \)-automata manipulation. In: Artho, C., Legay, A., Peled, D. (eds.) ATVA 2016. LNCS, vol. 9938, pp. 122–129. Springer, Heidelberg (2016). doi:10.1007/978-3-319-46520-3_8 CrossRefGoogle Scholar
  8. 8.
    Evangelista, S., Laarman, A., Petrucci, L., van de Pol, J.: Improved multi-core nested depth-first search. In: Chakraborty, S., Mukund, M. (eds.) Automated Technology for Verification and Analysis. LNCS, vol. 7561, pp. 269–283. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  9. 9.
    Evangelista, S., Petrucci, L., Youcef, S.: Parallel nested depth-first searches for LTL model checking. In: Bultan, T., Hsiung, P.-A. (eds.) ATVA 2011. LNCS, vol. 6996, pp. 381–396. Springer, Heidelberg (2011). doi:10.1007/978-3-642-24372-1_27 CrossRefGoogle Scholar
  10. 10.
    Fleischer, L.K., Hendrickson, B., Pınar, A.: On identifying strongly connected components in parallel. In: Rolim, J. (ed.) IPDPS 2000. LNCS, vol. 1800, pp. 505–511. Springer, Heidelberg (2000). doi:10.1007/3-540-45591-4_68 CrossRefGoogle Scholar
  11. 11.
    Gaiser, A., Schwoon, S.: Comparison of Algorithms for Checking Emptiness on Büchi Automata. CoRR abs/0910.3766 (2009)Google Scholar
  12. 12.
    Geldenhuys, J., Valmari, A.: Tarjan’s algorithm makes on-the-fly LTL verification more efficient. In: Jensen, K., Podelski, A. (eds.) Tools and Algorithms for the Construction and Analysis of Systems. LNCS, vol. 2988, pp. 205–219. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  13. 13.
    Giannakopoulou, D., Lerda, F.: From states to transitions: improving translation of LTL formulae to Büchi automata. In: Peled, D.A., Vardi, M.Y. (eds.) FORTE 2002. LNCS, vol. 2529, pp. 308–326. Springer, Heidelberg (2002). doi:10.1007/3-540-36135-9_20 CrossRefGoogle Scholar
  14. 14.
    Holzmann, G., Joshi, R., Groce, A.: Swarm verification techniques. IEEE Trans. Softw. Eng. 37(6), 845–857 (2011)CrossRefGoogle Scholar
  15. 15.
    Holzmann, G., Peled, D., Yannakakis, M.: On nested depth first search. In: Proceedings of the Second SPIN Workshop, vol. 32, pp. 81–89 (1996)Google Scholar
  16. 16.
    Hong, S., Rodia, N., Olukotun, K.: On fast parallel detection of strongly connected components (SCC) in small-world graphs. In: 2013 International Conference High Performance Computing, Networking, Storage and Analysis (SC), pp. 1–11 (2013)Google Scholar
  17. 17.
    Kant, G., Laarman, A., Meijer, J., Pol, J., Blom, S., Dijk, T.: LTSmin: high-performance language-independent model checking. In: Baier, C., Tinelli, C. (eds.) TACAS 2015. LNCS, vol. 9035, pp. 692–707. Springer, Heidelberg (2015). doi:10.1007/978-3-662-46681-0_61 Google Scholar
  18. 18.
    Kordon, F., Garavel, H., Hillah, L.M., Hulin-Hubard, F., Chiardo, G., Hamez, A., Jezequel, L., Miner, A., Meijer, J., Paviot-Adet, E., Racordon, D., Rodriguez, C., Rohr, C., Srba, J., Thierry-Mieg, Y., Trinh, G., Wolf, K.: Complete Results for the 2016 Edition of the Model Checking Contest (2016)Google Scholar
  19. 19.
    Kordon, F., Garavel, H., Hillah, L.M., Hulin-Hubard, F., Linard, A., Beccuti, M., Hamez, A., Lopez-Bobeda, E., Jezequel, L., Meijer, J., Paviot-Adet, E., Rodriguez, C., Rohr, C., Srba, J., Thierry-Mieg, Y., Wolf, K.: Complete Results for the 2015 Edition of the Model Checking Contest (2015)Google Scholar
  20. 20.
    Laarman, A., Langerak, R., Pol, J., Weber, M., Wijs, A.: Multi-core nested depth-first search. In: Bultan, T., Hsiung, P.-A. (eds.) ATVA 2011. LNCS, vol. 6996, pp. 321–335. Springer, Heidelberg (2011). doi:10.1007/978-3-642-24372-1_23 CrossRefGoogle Scholar
  21. 21.
    Laarman, A., van de Pol, J.: Variations on multi-core nested depth-first search. In: Barnat, J., Heljanko, K. (eds.) PDMC 2011. EPTCS, vol. 72, pp. 13–28 (2011)Google Scholar
  22. 22.
    Laarman, A., Pol, J., Weber, M.: Multi-core LTSmin: marrying modularity and scalability. In: Bobaru, M., Havelund, K., Holzmann, G.J., Joshi, R. (eds.) NFM 2011. LNCS, vol. 6617, pp. 506–511. Springer, Heidelberg (2011). doi:10.1007/978-3-642-20398-5_40 CrossRefGoogle Scholar
  23. 23.
    Lowe, G.: Concurrent depth-first search algorithms based on Tarjan’s algorithm. Int. J. Softw. Tools Technol. Transf. 18(2), 1–19 (2015)Google Scholar
  24. 24.
    Manna, Z., Pnueli, A.: A hierarchy of temporal properties. In: Proceedings of the Sixth Annual ACM Symposium on Principles of Distributed Computing, PODC 1987, p. 205. ACM (1987)Google Scholar
  25. 25.
    Orzan, S.: On Distributed Verification and Verified Distribution. Ph.D. thesis (2004)Google Scholar
  26. 26.
    Pelánek, R.: BEEM: benchmarks for explicit model checkers. In: Bošnački, D., Edelkamp, S. (eds.) SPIN 2007. LNCS, vol. 4595, pp. 263–267. Springer, Heidelberg (2007). doi:10.1007/978-3-540-73370-6_17 CrossRefGoogle Scholar
  27. 27.
    Pelánek, R.: Properties of state spaces and their applications. Int. J. Softw. Tools Technol. Transf. 10(5), 443–454 (2008)CrossRefGoogle Scholar
  28. 28.
    Rao, V.N., Kumar, V.: Superlinear speedup in parallel state-space search. In: Nori, K.V., Kumar, S. (eds.) Foundations of Software Technology and Theoretical Computer Science. LNCS, vol. 338, pp. 161–174. Springer, Heidelberg (1988)CrossRefGoogle Scholar
  29. 29.
    Renault, E., Duret-Lutz, A., Kordon, F., Poitrenaud, D.: Parallel explicit model checking for generalized Büchi automata. In: Baier, C., Tinelli, C. (eds.) TACAS 2015. LNCS, vol. 9035, pp. 613–627. Springer, Heidelberg (2015). doi:10.1007/978-3-662-46681-0_56 Google Scholar
  30. 30.
    Renault, E., Duret-Lutz, A., Kordon, F., Poitrenaud, D.: Variations on parallel explicit emptiness checks for generalized Büchi automata. Int. J. Softw. Tools Technol. Transf. 1–21 (2016). http://link.springer.com/journal/10009/onlineFirst/page/1
  31. 31.
    Schudy, W.: Finding strongly connected components in parallel using O(log2n) reachability queries. In: Proceedings of the Twentieth Annual Symposium on Parallelism in Algorithms and Architectures, SPAA 2008, pp. 146–151. ACM (2008)Google Scholar
  32. 32.
    Schwoon, S., Esparza, J.: A note on on-the-fly verification algorithms. In: Halbwachs, N., Zuck, L.D. (eds.) TACAS 2005. LNCS, vol. 3440, pp. 174–190. Springer, Heidelberg (2005). doi:10.1007/978-3-540-31980-1_12 CrossRefGoogle Scholar
  33. 33.
    Slota, G.M., Rajamanickam, S., Madduri, K.: BFS and coloring-based parallel algorithms for strongly connected components and related problems. In: 2014 IEEE 28th International Parallel and Distributed Processing Symposium, pp. 550–559 (2014)Google Scholar
  34. 34.
    Tarjan, R.E.: Depth-first search and linear graph algorithms. SIAM J. Comput. 1(2), 146–160 (1972)MathSciNetCrossRefMATHGoogle Scholar
  35. 35.
    Vardi, M.Y., Wolper, P.: An automata-theoretic approach to automatic program verification. In: Proceedings of the First Symposium on Logic in Computer Science, pp. 322–331. IEEE Computer Society (1986)Google Scholar
  36. 36.
    Černá, I., Pelánek, R.: Relating hierarchy of temporal properties to model checking. In: Rovan, B., Vojtáš, P. (eds.) MFCS 2003. LNCS, vol. 2747, pp. 318–327. Springer, Heidelberg (2003). doi:10.1007/978-3-540-45138-9_26 CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.Formal Methods and ToolsUniversity of TwenteEnschedeThe Netherlands

Personalised recommendations