Skip to main content

Parity Games on Bounded Phase Multi-pushdown Systems

  • Conference paper
  • First Online:
Networked Systems (NETYS 2017)

Part of the book series: Lecture Notes in Computer Science ((LNCCN,volume 10299))

Included in the following conference series:

Abstract

In this paper we address the problem of solving parity games over the configuration graphs of bounded phase multi-pushdown systems. A non-elementary decision procedure was proposed for this problem by A. Seth. In this paper, we provide a simple and inductive construction to solve this problem. We also prove a non-elementary lower-bound, answering a question posed by A. Seth.

The authors acknowledge partial support by Indo-French Project AVeCSo, TCS-Fellowship, Indo-Swedish DST-VR Project P-02/2014, Infosys Foundation.

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

Access this chapter

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 EPUB and 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

References

  1. Cachat, T.: Uniform solution of parity games on prefix-recognizable graphs. Electr. Notes Theor. Comput. Sci. 68, 1–15 (2002)

    MATH  Google Scholar 

  2. Emerson, E.A., Jutla, C.S.: Tree automata, mu-calculus and determinacy (extended abstract). In: 32nd Annual Symposium on Foundations of Computer Science, San Juan, Puerto Rico, 1–4 October (1991)

    Google Scholar 

  3. Kupferman, O., Piterman, N., Vardi, M.Y.: An automata-theoretic approach to infinite-state systems. In: Manna, Z., Peled, D.A. (eds.) Time for Verification. LNCS, vol. 6200, pp. 202–259. Springer, Heidelberg (2010). doi:10.1007/978-3-642-13754-9_11

    Chapter  Google Scholar 

  4. Martin, D.A.: Borel determinacy. Ann. Math. 102, 363–371 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  5. Qadeer, S., Rehof, J.: Context-bounded model checking of concurrent software. In: Halbwachs, N., Zuck, L.D. (eds.) TACAS 2005. LNCS, vol. 3440, pp. 93–107. Springer, Heidelberg (2005). doi:10.1007/978-3-540-31980-1_7

    Chapter  Google Scholar 

  6. Saivasan, P.: Analysis of Automata-theoretic models of Concurrent Recursive Programs. Ph.D. thesis, Chennai Mathematical Institute (2016)

    Google Scholar 

  7. Serre, O.: Note on winning positions on pushdown games with [omega]-regular conditions. Inf. Process. Lett. 85, 285–291 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  8. Seth, A.: Games on multi-stack pushdown systems. In: Artemov, S., Nerode, A. (eds.) LFCS 2009. LNCS, vol. 5407, pp. 395–408. Springer, Heidelberg (2008). doi:10.1007/978-3-540-92687-0_27

    Chapter  Google Scholar 

  9. Stockmeyer, L.J.: The Complexity of Decision Problems in Automata Theory and Logic. Ph.D. thesis. MIT, Cambridge (1974)

    Google Scholar 

  10. Torre, S.L., Madhusudan, P., Parlato, G.: A robust class of context-sensitive languages. In: LICS. IEEE Computer Society (2007)

    Google Scholar 

  11. Torre, S., Madhusudan, P., Parlato, G.: Reducing context-bounded concurrent reachability to sequential reachability. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 477–492. Springer, Heidelberg (2009). doi:10.1007/978-3-642-02658-4_36

    Chapter  Google Scholar 

  12. Walukiewicz, I.: Pushdown processes: games and model checking. In: Alur, R., Henzinger, T.A. (eds.) CAV 1996. LNCS, vol. 1102, pp. 62–74. Springer, Heidelberg (1996). doi:10.1007/3-540-61474-5_58

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Prakash Saivasan .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Atig, M.F., Bouajjani, A., Narayan Kumar, K., Saivasan, P. (2017). Parity Games on Bounded Phase Multi-pushdown Systems. In: El Abbadi, A., Garbinato, B. (eds) Networked Systems. NETYS 2017. Lecture Notes in Computer Science(), vol 10299. Springer, Cham. https://doi.org/10.1007/978-3-319-59647-1_21

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-59647-1_21

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-59646-4

  • Online ISBN: 978-3-319-59647-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics