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On Boundedness Problems for Pushdown Vector Addition Systems

  • Jérôme Leroux
  • Grégoire SutreEmail author
  • Patrick Totzke
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9328)

Abstract

We study pushdown vector addition systems, which are synchronized products of pushdown automata with vector addition systems. The question of the boundedness of the reachability set for this model can be refined into two decision problems that ask if infinitely many counter values or stack configurations are reachable, respectively. Counter boundedness seems to be the more intricate problem. We show decidability in exponential time for one-dimensional systems. The proof is via a small witness property derived from an analysis of derivation trees of grammar-controlled vector addition systems.

Keywords

Production Rule Coverability Problem Exponential Time Parse Tree Reachability Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Ball, T., Majumdar, R., Millstein, T.D., Rajamani, S.K.: Automatic predicate abstraction of C programs. In: PLDI, pp. 203–213 (2001)Google Scholar
  2. 2.
    Bouajjani, A., Mayr, R.: Model checking lossy vector addition systems. In: Meinel, C., Tison, S. (eds.) STACS 1999. LNCS, vol. 1563, pp. 323–333. Springer, Heidelberg (1999) CrossRefGoogle Scholar
  3. 3.
    Dassow, J., Pun, G., Salomaa, A.: Grammars with controlled derivations. In: Handbook of Formal Languages, pp. 101–154 (1997)Google Scholar
  4. 4.
    Fearnley, J., Jurdziński, M.: Reachability in two-clock timed automata is PSPACE-complete. In: Fomin, F.V., Freivalds, R., Kwiatkowska, M., Peleg, D. (eds.) ICALP 2013, Part II. LNCS, vol. 7966, pp. 212–223. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  5. 5.
    Karp, R.M., Miller, R.E.: Parallel program schemata. J. Comput. Syst. Sci. 3(2), 147–195 (1969)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Kosaraju, S.R.: Decidability of reachability in vector addition systems (preliminary version). In: STOC, pp. 267–281 (1982)Google Scholar
  7. 7.
    Lazic, R.: The reachability problem for vector addition systems with a stack is not elementary. CoRR abs/1310.1767 (2013)Google Scholar
  8. 8.
    Leroux, J., Praveen, M., Sutre, G.: Hyper-ackermannian bounds for pushdown vector addition systems. In: CSL/LICS (2014)Google Scholar
  9. 9.
    Leroux, J., Schmitz, S.: Demystifying reachability in vector addition systems. In: LICS (2015)Google Scholar
  10. 10.
    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) CrossRefGoogle Scholar
  11. 11.
    Lipton, R.J.: The reachability problem requires exponential space. Tech. Rep. 63, Yale University (January 1976)Google Scholar
  12. 12.
    Mayr, E.W.: An algorithm for the general Petri net reachability problem. In: STOC. pp. 238–246 (1981)Google Scholar
  13. 13.
    Rackoff, C.: The covering and boundedness problems for vector addition systems. TCS 6(2), 223–231 (1978)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Jérôme Leroux
    • 1
  • Grégoire Sutre
    • 1
    Email author
  • Patrick Totzke
    • 2
  1. 1.University of Bordeaux and CNRS, LaBRI, UMR 5800TalenceFrance
  2. 2.Department of Computer ScienceUniversity of WarwickCoventryUK

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