Skip to main content
SpringerLink
Log in

Short Witnesses and Accepting Lassos in ω-Automata

  • Conference paper
Language and Automata Theory and Applications (LATA 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6031))

Abstract

Emptiness checking of ω-automata is a fundamental part of the automata-theoretic toolbox and is frequently applied in many applications, most notably verification of reactive systems. In this particular application, the capability to extract accepted words or alternatively accepting runs in case of non-emptiness is particularly useful, as these have a diagnostic value. However, non-optimised such words or runs can become huge, limiting their usability in practice, thus solutions with a small representation should be preferred. In this paper, we review the known results on obtaining these and complete the complexity landscape for all commonly used automaton types. We also prove upper and lower bounds on the approximation hardness of these problems.

This work was supported by the German Research Foundation (DFG) within the program “Performance Guarantees for Computer Systems” and the Transregional Collaborative Research Center “Automatic Verification and Analysis of Complex Systems” (SFB/TR 14 AVACS).

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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. Baier, C., Katoen, J.P.: Principles of Model Checking. MIT Press, Cambridge (2008)

    MATH  Google Scholar 

  2. Büchi, J.R.: On a decision method in restricted second-order arithmetic. In: Proc. 1960 Int. Congr. for Logic, Methodology, and Philosophy of Science, pp. 1–11 (1962)

    Google Scholar 

  3. Clarke, E.M., Emerson, E.A.: Design and synthesis of synchronization skeletons using branching-time temporal logic. In: Kozen, D. (ed.) Logic of Programs 1981. LNCS, vol. 131, pp. 52–71. Springer, Heidelberg (1981)

    Chapter  Google Scholar 

  4. Clarke, E.M., Grumberg, O., McMillan, K.L., Zhao, X.: Efficient generation of counterexamples and witnesses in symbolic model checking. In: DAC, pp. 427–432 (1995)

    Google Scholar 

  5. Dinur, I., Guruswami, V., Khot, S., Regev, O.: A new multilayered PCP and the hardness of hypergraph vertex cover. SIAM J. Comput. 34(5), 1129–1146 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  6. Engebretsen, L., Karpinski, M.: Approximation hardness of TSP with bounded metrics. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds.) ICALP 2001. LNCS, vol. 2076, pp. 201–212. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  7. Farwer, B.: ω-automata. In: [10], pp. 3–20

    Google Scholar 

  8. Frieze, A.M., Galbiati, G., Maffioli, F.: On the worst-case performance of some algorithms for the asymmetric traveling salesman problem. Networks 12(1), 23–39 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  9. Gastin, P., Moro, P.: Minimal counterexample generation for SPIN. In: Bošnački, D., Edelkamp, S. (eds.) SPIN 2007. LNCS, vol. 4595, pp. 24–38. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  10. Grädel, E., Thomas, W., Wilke, T. (eds.): Automata, Logics, and Infinite Games: A Guide to Current Research. LNCS, vol. 2500. Springer, Heidelberg (2002)

    MATH  Google Scholar 

  11. Groce, A., Visser, W.: What went wrong: Explaining counterexamples. In: Ball, T., Rajamani, S.K. (eds.) SPIN 2003. LNCS, vol. 2648, pp. 121–135. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  12. Grumberg, O., Veith, H. (eds.): 25 Years of Model Checking - History, Achievements, Perspectives. LNCS, vol. 5000. Springer, Heidelberg (2008)

    MATH  Google Scholar 

  13. Hansen, H., Geldenhuys, J.: Cheap and small counterexamples. In: Cerone, A., Gruner, S. (eds.) SEFM, pp. 53–62. IEEE Computer Society, Los Alamitos (2008)

    Google Scholar 

  14. Henzinger, M.R., Telle, J.A.: Faster algorithms for the nonemptiness of Streett automata and for communication protocol pruning. In: Karlsson, R.G., Lingas, A. (eds.) SWAT, pp. 16–27. Springer, Heidelberg (1996)

    Google Scholar 

  15. Khot, S., Regev, O.: Vertex cover might be hard to approximate to within 2-ε. J. Comput. Syst. Sci. 74(3), 335–349 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  16. Kupferman, O., Sheinvald-Faragy, S.: Finding shortest witnesses to the nonemptiness of automata on infinite words. In: Baier, C., Hermanns, H. (eds.) CONCUR 2006. LNCS, vol. 4137, pp. 492–508. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  17. Mitra, R.S.: Strategies for mainstream usage of formal verification. In: Fix, L. (ed.) DAC, pp. 800–805. ACM, New York (2008)

    Chapter  Google Scholar 

  18. Safra, S.: Complexity of Automata on Infinite Objects. PhD thesis, Weizmann Institute of Science, Rehovot, Israel (March 1989)

    Google Scholar 

  19. Schwoon, S., Esparza, J.: A note on on-the-fly verification algorithms. In: Halbwachs, N., Zuck, L.D. (eds.) TACAS 2005. LNCS, vol. 3440, pp. 174–190. Springer, Heidelberg (2005)

    Google Scholar 

  20. Vardi, M.Y.: An automata-theoretic approach to linear temporal logic. In: Proceedings of the VIII Banff Higher order workshop conference on Logics for concurrency: structure versus automata, pp. 238–266. Springer, New York (1996)

    Google Scholar 

  21. Wegener, I.: Complexity Theory. In: Exploring the Limits of Efficient Algorithms. Springer, Heidelberg (2004)

    Google Scholar 

  22. Woodcock, J., Larsen, P.G., Bicarregui, J., Fitzgerald, J.S.: Formal methods: Practice and experience. ACM Comput. Surv. 41(4) (2009)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Reactive Systems Group, Saarland University,  

    Rüdiger Ehlers

Authors
  1. Rüdiger Ehlers
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Research Group on Mathematical Linguistics, Universitat Rovira i Virgili, Avinguda Catalunya, 35, 43002, Tarragona, Spain

    Adrian-Horia Dediu  & Carlos Martín-Vide  & 

  2. Fachbereich IV - Informatik, Universität Trier, Campus II, Behringstraße, 54286, Trier, Germany

    Henning Fernau

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ehlers, R. (2010). Short Witnesses and Accepting Lassos in ω-Automata. In: Dediu, AH., Fernau, H., Martín-Vide, C. (eds) Language and Automata Theory and Applications. LATA 2010. Lecture Notes in Computer Science, vol 6031. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13089-2_22

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-13089-2_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13088-5

  • Online ISBN: 978-3-642-13089-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation