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Revisiting Ackermann-Hardness for Lossy Counter Machines and Reset Petri Nets

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Mathematical Foundations of Computer Science 2010 (MFCS 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6281))

Abstract

We prove that coverability and termination are not primitive-recursive for lossy counter machines and for Reset Petri nets.

Work supported by the Agence Nationale de la Recherche, grant ANR-06-SETIN-001.

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References

  1. Amadio, R., Meyssonnier, C.: On decidability of the control reachability problem in the asynchronous π-calculus. Nordic Journal of Computing 9(2), 70–101 (2002)

    MATH  MathSciNet  Google Scholar 

  2. Araki, T., Kasami, T.: Some decision problems related to the reachability problem for Petri nets. Theoretical Computer Science 3(1), 85–104 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  3. Chambart, P., Schnoebelen, P.: The ordinal recursive complexity of lossy channel systems. In: Proc. LICS 2008, pp. 205–216. IEEE Comp. Soc. Press, Los Alamitos (2008)

    Google Scholar 

  4. Chambart, P., Schnoebelen, P.: Pumping and counting on the Regular Post Embedding Problem. In: Proc. ICALP 2010. LNCS. Springer, Heidelberg (2010)

    Google Scholar 

  5. Ciardo, G.: Petri nets with marking-dependent arc cardinality: Properties and analysis. In: Valette, R. (ed.) ICATPN 1994. LNCS, vol. 815, pp. 179–198. Springer, Heidelberg (1994)

    Google Scholar 

  6. Demri, S.: Linear-time temporal logics with Presburger constraints: An overview. J. Applied Non-Classical Logics 16(3-4), 311–347 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  7. Demri, S., Lazić, R.: LTL with the freeze quantifier and register automata. In: Proc. LICS 2006, pp. 17–26. IEEE Computer Society Press, Los Alamitos (2006)

    Google Scholar 

  8. Dufourd, C., Finkel, A., Schnoebelen, P.: Reset nets between decidability and undecidability. In: Larsen, K.G., Skyum, S., Winskel, G. (eds.) ICALP 1998. LNCS, vol. 1443, pp. 103–115. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  9. Dufourd, C., Jančar, P., Schnoebelen, P.: Boundedness of Reset P/T nets. In: Wiedermann, J., Van Emde Boas, P., Nielsen, M. (eds.) ICALP 1999. LNCS, vol. 1644, pp. 301–310. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  10. Fairtlough, M.V., Wainer, S.S.: Hierarchies of provably recursive functions. In: Handbook of Proof Theory. Studies in Logic, vol. 137, pp. 149–207. North-Holland, Amsterdam (1998)

    Chapter  Google Scholar 

  11. Figueira, D., Figueira, S., Schmitz, S., Schnoebelen, P.: Ackermann and primitive-recursive upper bounds with Dickson’s lemma. In: Preparation (2010)

    Google Scholar 

  12. Figueira, D., Segoufin, L.: Future-looking logics on data words and trees. In: Královič, R., Niwiński, D. (eds.) MFCS 2009. LNCS, vol. 5734, pp. 331–343. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  13. Finkel, A., Raskin, J.-F., Samuelides, M., Van Begin, L.: Monotonic extensions of Petri nets: Forward and backward search revisited. In: Proc. INFINITY 2002. Electronic Notes in Theoretical Computer Science, vol. 68(6), pp. 121–144 (2003)

    Google Scholar 

  14. Jurdziński, M., Lazić, R.: Alternation-free modal μ-calculus for data trees. In: Proc. LICS 2007, pp. 131–140. IEEE Comp. Soc. Press, Los Alamitos (2007)

    Google Scholar 

  15. Jurdziński, T.: Leftist grammars are nonprimitive recursive. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part II. LNCS, vol. 5126, pp. 51–62. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  16. Mayr, R.: Undecidable problems in unreliable computations. Theoretical Computer Science 297(1-3), 337–354 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  17. McAloon, K.: Petri nets and large finite sets. Theoretical Computer Science 32(1-2), 173–183 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  18. Schnoebelen, P.: Verifying lossy channel systems has nonprimitive recursive complexity. Information Processing Letters 83(5), 251–261 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  19. Schnoebelen, P.: Lossy counter machines decidability cheat sheet. In: RP 2010. LNCS, vol. 6227. Springer, Heidelberg (2010)

    Google Scholar 

  20. Tan, T.: On pebble automata for data languages with decidable emptiness problem. In: Královič, R., Niwiński, D. (eds.) MFCS 2009. LNCS, vol. 5734, pp. 712–723. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. LSV, ENS Cachan, CNRS, 61, av. Pdt. Wilson, F-94230, Cachan, France

    Philippe Schnoebelen

Authors
  1. Philippe Schnoebelen
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Editor information

Editors and Affiliations

  1. Falculty of Informatics, Masaryk University, Botanicka 68a, 602 00, Brno, Czech Republic

    Petr Hliněný

  2. Faculty of Informatics, Masaryk University, Botanicka 68a, 602 00, Brno, Czech Republic

    Antonín Kučera

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Schnoebelen, P. (2010). Revisiting Ackermann-Hardness for Lossy Counter Machines and Reset Petri Nets. In: Hliněný, P., Kučera, A. (eds) Mathematical Foundations of Computer Science 2010. MFCS 2010. Lecture Notes in Computer Science, vol 6281. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15155-2_54

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  • DOI: https://doi.org/10.1007/978-3-642-15155-2_54

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15154-5

  • Online ISBN: 978-3-642-15155-2

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