Skip to main content
SpringerLink
Log in

Alternating Vector Addition Systems with States

  • Conference paper
Mathematical Foundations of Computer Science 2014 (MFCS 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8634))

Abstract

Alternating vector addition systems are obtained by equipping vector addition systems with states (VASS) with ‘fork’ rules, and provide a natural setting for infinite-arena games played over a VASS. Initially introduced in the study of propositional linear logic, they have more recently gathered attention in the guise of multi-dimensional energy games for quantitative verification and synthesis.

We show that establishing who is the winner in such a game with a state reachability objective is 2-ExpTime-complete. As a further application, we show that the same complexity result applies to the problem of whether a VASS is simulated by a finite-state system.

Work funded in part by the ANR grant 11-BS02-001-01 ReacHard.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abdulla, P.A., Atig, M.F., Hofman, P., Mayr, R., Kumar, K.N., Totzke, P.: Infinite-state energy games. In: CSL-LICS. ACM (to appear, 2014)

    Google Scholar 

  2. Abdulla, P.A., Bouajjani, A., d’Orso, J.: Deciding monotonic games. In: Baaz, M., Makowsky, J.A. (eds.) CSL 2003. LNCS, vol. 2803, pp. 1–14. Springer, Heidelberg (2003)

    Google Scholar 

  3. Abdulla, P.A., Mayr, R., Sangnier, A., Sproston, J.: Solving parity games on integer vectors. In: D’Argenio, P.R., Melgratti, H. (eds.) CONCUR 2013 – Concurrency Theory. LNCS, vol. 8052, pp. 106–120. Springer, Heidelberg (2013)

    Google Scholar 

  4. Bérard, B., Haddad, S., Sassolas, M., Sznajder, N.: Concurrent games on VASS with inhibition. In: Koutny, M., Ulidowski, I. (eds.) CONCUR 2012. LNCS, vol. 7454, pp. 39–52. Springer, Heidelberg (2012)

    Google Scholar 

  5. Brázdil, T., Jančar, P., Kučera, A.: Reachability games on extended vector addition systems with states. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds.) ICALP 2010. LNCS, vol. 6199, pp. 478–489. Springer, Heidelberg (2010)

    Google Scholar 

  6. Chaloupka, J.: Z-reachability problem for games on 2-dimensional vector addition systems with states is in P. Fund. Inform. 123(1), 15–42 (2013)

    MATH  MathSciNet  Google Scholar 

  7. Chatterjee, K., Doyen, L., Henzinger, T.A., Raskin, J.F.: Generalized mean-payoff and energy games. In: FSTTCS 2010. LIPIcs, vol. 8, pp. 505–516. LZI (2010)

    Google Scholar 

  8. Demri, S., Jurdziński, M., Lachish, O., Lazić, R.: The covering and boundedness problems for branching vector addition systems. J. Comput. Syst. Sci. 79(1), 23–38 (2012)

    Article  Google Scholar 

  9. Jančar, P., Moller, F.: Checking regular properties of Petri nets. In: Lee, I., Smolka, S.A. (eds.) CONCUR 1995. LNCS, vol. 962, pp. 348–362. Springer, Heidelberg (1995)

    Google Scholar 

  10. Kanovich, M.I.: Petri nets, Horn programs, linear logic and vector games. Ann. Pure App. Logic 75(1-2), 107–135 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  11. Kučera, A., Mayr, R.: Simulation preorder over simple process algebras. Inform. and Comput. 173(2), 184–198 (2002)

    MATH  MathSciNet  Google Scholar 

  12. Lasota, S.: Exp Space lower bounds for the simulation preorder between a communication-free Petri net and a finite-state system. Inf. Process. Lett. 109(15), 850–855 (2009)

    MATH  MathSciNet  Google Scholar 

  13. Lincoln, P., Mitchell, J., Scedrov, A., Shankar, N.: Decision problems for propositional linear logic. Ann. Pure App. Logic 56(1-3), 239–311 (1992)

    MATH  MathSciNet  Google Scholar 

  14. Lipton, R.: The reachability problem requires exponential space. Tech. Rep. 62, Yale University (1976)

    Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

  16. Raskin, J.F., Samuelides, M., Begin, L.V.: Games for counting abstractions. In: AVoCS 2004. ENTCS, vol. 128(6), pp. 69–85. Elsevier (2005)

    Google Scholar 

  17. Rosier, L., Yen, H.C.: A multiparameter analysis of the boundedness problem for vector addition systems. J. Comput. Syst. Sci. 32(1), 105–135 (1986)

    MATH  MathSciNet  Google Scholar 

  18. Yen, H.C., Chen, C.L.: On minimal elements of upward-closed sets. Theor. Comput. Sci. 410(24-25), 2442–2452 (2009)

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. LSV, ENS Cachan & CNRS & INRIA, France

    Jean-Baptiste Courtois & Sylvain Schmitz

Authors
  1. Jean-Baptiste Courtois
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sylvain Schmitz
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Faculty of Informatics, Eötvös Loránd University, Pázmány Péter sétány 1/C, 1117, Budapest, Hungary

    Erzsébet Csuhaj-Varjú

  2. Fakultät für Informatik und Automatisierung, Technische Universität Ilmenau, Helmholtzplatz, 598693, Ilmenau, Germany

    Martin Dietzfelbinger

  3. Institute of Informatics, Szeged University, Tisza Lajos krt. 103, 6720, Szeged, Hungary

    Zoltán Ésik

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer-Verlag GmbH Berlin Heidelberg

About this paper

Cite this paper

Courtois, JB., Schmitz, S. (2014). Alternating Vector Addition Systems with States. In: Csuhaj-Varjú, E., Dietzfelbinger, M., Ésik, Z. (eds) Mathematical Foundations of Computer Science 2014. MFCS 2014. Lecture Notes in Computer Science, vol 8634. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44522-8_19

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-44522-8_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-44521-1

  • Online ISBN: 978-3-662-44522-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation