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What Makes Petri Nets Harder to Verify: Stack or Data?

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Concurrency, Security, and Puzzles

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 10160))

Abstract

We show how the yardstick construction of Stockmeyer, also developed as counter bootstrapping by Lipton, can be adapted and extended to obtain new lower bounds for the coverability problem for two prominent classes of systems based on Petri nets: Ackermann-hardness for unordered data Petri nets, and Tower-hardness for pushdown vector addition systems.

Supported by the EPSRC, grants EP/M011801/1 and EP/M027651/1, and by the Royal Society, grant IE150122.

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References

  1. Abdulla, P.A., Čerāns, K., Jonsson, B., Tsay, Y.-K.: Algorithmic analysis of programs with well quasi-ordered domains. Inform. Comput. 160(1–2), 109–127 (2000)

    Google Scholar 

  2. Atig, M.F., Ganty, P.: Approximating Petri net reachability along context-free traces. In: FSTTCS. LIPIcs, vol. 13, pp. 152–163. LZI (2011)

    Google Scholar 

  3. Bojańczyk, M., Klin, B., Lasota, S.: Automata theory in nominal sets. Logic. Meth. Comput. Sci. 10(3:4), 1–44 (2014)

    MathSciNet  MATH  Google Scholar 

  4. Chambart, P., Schnoebelen, P.: The ordinal recursive complexity of lossy channel systems. In: LICS, pp. 205–216. IEEE Press (2008)

    Google Scholar 

  5. Decker, N., Thoma, D.: On freeze LTL with ordered attributes. In: Jacobs, B., Löding, C. (eds.) FoSSaCS 2016. LNCS, vol. 9634, pp. 269–284. Springer, Heidelberg (2016). doi:10.1007/978-3-662-49630-5_16

    Chapter  Google Scholar 

  6. Figueira, D., Figueira, S., Schmitz, S., Schnoebelen, P.: Ackermannian and primitive-recursive bounds with Dickson’s Lemma. In: LICS, pp. 269–278. IEEE Press (2011)

    Google Scholar 

  7. Finkel, A., McKenzie, P., Picaronny, C.: A well-structured framework for analysing Petri net extensions. Inform. Comput. 195(1–2), 1–29 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  8. Finkel, A., Schnoebelen, P.: Well-structured transition systems everywhere! Theor. Comput. Sci. 256(1–2), 63–92 (2001)

    Google Scholar 

  9. Haase, C., Schmitz, S., Schnoebelen, P.: The power of priority channel systems. Logic. Meth. Comput. Sci. 10(4:4), 1–39 (2014)

    MathSciNet  MATH  Google Scholar 

  10. Haddad, S., Schmitz, S., Schnoebelen, P.: The ordinal recursive complexity of timed-arc Petri nets, data nets, and other enriched nets. In: LICS, pp. 355–364. IEEE Press (2012)

    Google Scholar 

  11. Hofman, P., Lasota, S., Lazić, R., Leroux, J., Schmitz, S., Totzke, P.: Coverability trees for Petri nets with unordered data. In: Jacobs, B., Löding, C. (eds.) FoSSaCS 2016. LNCS, vol. 9634, pp. 445–461. Springer, Heidelberg (2016). doi:10.1007/978-3-662-49630-5_26

    Chapter  Google Scholar 

  12. Hofman, P., Leroux, J., Totzke, P.: Linear combinations of unordered data vectors. arXiv:1610.01470 [cs.LO] (2016)

  13. Jensen, K.: Coloured Petri Nets - Basic Concepts, Analysis Methods and Practical Use - Volume 1. Monographs in Theoretical Computer Science. An EATCS Series, 2nd edn. Springer, Heidelberg (1996)

    Book  MATH  Google Scholar 

  14. Lazić, R.: The reachability problem for vector addition systems with a stack is not elementary. arXiv:1310.1767 [cs.FL] (2013)

  15. Lazić, R., Newcomb, T., Ouaknine, J., Roscoe, A.W., Worrell, J.: Nets with tokens which carry data. Fund. Inform. 88(3), 251–274 (2008)

    MathSciNet  MATH  Google Scholar 

  16. Lazić, R., Ouaknine, J., Worrell, J.: Zeno, Hercules, and the Hydra: Safety metric temporal logic is Ackermann-complete. ACM Trans. Comput. Logic 17(3), 1–27 (2016). Article 16

    MathSciNet  Google Scholar 

  17. Lazić, R., Schmitz, S.: The complexity of coverability in \(\nu \)-Petri nets. In: LICS, pp. 467–476. ACM (2016)

    Google Scholar 

  18. Leroux, J., Praveen, M., Sutre, G.: Hyper-Ackermannian bounds for pushdown vector addition systems. In: CSL-LICS, pp. 63:1–63:10. ACM (2014)

    Google Scholar 

  19. Leroux, J., Sutre, G., Totzke, P.: On boundedness problems for pushdown vector addition systems. In: Bojańczyk, M., Lasota, S., Potapov, I. (eds.) RP 2015. LNCS, vol. 9328, pp. 101–113. Springer, Heidelberg (2015). doi:10.1007/978-3-319-24537-9_10

    Chapter  Google Scholar 

  20. Leroux, J., Sutre, G., Totzke, P.: On the coverability problem for pushdown vector addition systems in one dimension. In: Halldórsson, M.M., Iwama, K., Kobayashi, N., Speckmann, B. (eds.) ICALP 2015. LNCS, vol. 9135, pp. 324–336. Springer, Heidelberg (2015). doi:10.1007/978-3-662-47666-6_26

    Google Scholar 

  21. Lipton, R.: The reachability problem requires exponential space. Technical report 62. Yale University (1976)

    Google Scholar 

  22. Rackoff, C.: The covering and boundedness problems for vector addition systems. Theor. Comput. Sci. 6(2), 223–231 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  23. Rosa-Velardo, F.: Ordinal recursive complexity of unordered data nets. Technical report TR-4-14. Universidad Complutense de Madrid (2014)

    Google Scholar 

  24. Rosa-Velardo, F., de Frutos-Escrig, D.: Decidability and complexity of Petri nets with unordered data. Theor. Comput. Sci. 412(34), 4439–4451 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  25. Schmitz, S.: Complexity hierarchies beyond Elementary. ACM Trans. Comput. Theor. 8(1), 1–36 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  26. Schmitz, S., Schnoebelen, P.: Multiply-recursive upper bounds with Higman’s lemma. In: Aceto, L., Henzinger, M., Sgall, J. (eds.) ICALP 2011. LNCS, vol. 6756, pp. 441–452. Springer Berlin Heidelberg, Berlin, Heidelberg (2011). doi:10.1007/978-3-642-22012-8_35

    Chapter  Google Scholar 

  27. Schnoebelen, P.: Revisiting Ackermann-hardness for lossy counter machines and reset Petri nets. In: Hliněný, P., Kučera, A. (eds.) MFCS 2010. LNCS, vol. 6281, pp. 616–628. Springer, Heidelberg (2010). doi:10.1007/978-3-642-15155-2_54

    Chapter  Google Scholar 

  28. Stockmeyer, L.J.: The complexity of decision procedures in Automata Theory and Logic, Ph.D. thesis. MIT, Project MAC TR-133 (1974)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, DIMAP, University of Warwick, Coventry, UK

    Ranko Lazić

  2. LFCS, School of Informatics, University of Edinburgh, Edinburgh, UK

    Patrick Totzke

Authors
  1. Ranko Lazić
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  2. Patrick Totzke
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Correspondence to Ranko Lazić .

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Editors and Affiliations

  1. University of Oxford, Oxford, United Kingdom

    Thomas Gibson-Robinson

  2. University of Oxford, Oxford, United Kingdom

    Philippa Hopcroft

  3. University of Warwick, Coventry, United Kingdom

    Ranko Lazić

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Lazić, R., Totzke, P. (2017). What Makes Petri Nets Harder to Verify: Stack or Data?. In: Gibson-Robinson, T., Hopcroft, P., Lazić, R. (eds) Concurrency, Security, and Puzzles. Lecture Notes in Computer Science(), vol 10160. Springer, Cham. https://doi.org/10.1007/978-3-319-51046-0_8

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  • DOI: https://doi.org/10.1007/978-3-319-51046-0_8

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