Skip to main content

Model checking the full modal mu-calculus for infinite sequential processes

  • Session 10: Logic and Verification
  • Conference paper
  • First Online:
Automata, Languages and Programming (ICALP 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1256))

Included in the following conference series:

Abstract

In this paper we develop a new exponential algorithm for model-checking infinite sequential processes, including context-free processes, pushdown processes, and regular graphs, that decides the full modal mu-calculus. Whereas the actual model checking algorithm results from considering conditional semantics together with backtracking caused by alternation, the corresponding correctness proof requires a stronger framework, which uses dynamic environments modelled by finite-state automata.

This work was supported during my stay at IRISA by the European Community under HCM grant ERBCHBGCT 920017, and during my stay at the LFCS by the DAAD under grant D/95/14834 of the NATO science committee.

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. O. Burkart and J. Esparza. More Infinite Results. In INFINITY '96, volume 6 of ENTCS, 23 pages. Elsevier Science B.V., 1997.

    Google Scholar 

  2. O. Burkart and Y.-M. Quemener. Model-Checking of Infinite Graphs Defined by Graph Grammars. In INFINITY '96, volume 6 of ENTCS, 15 pages. Elsevier Science B.V., 1997.

    Google Scholar 

  3. J.C. Bradfield. The Modal mu-Calculus Alternation Hierarchy is Strict. In CONCUR '96, LNCS 1119, pages 233–246. Springer, 1996.

    Google Scholar 

  4. O. Burkart and B. Steffen. Model Checking for Context-Free Processes. In CONCUR '92, LNCS 630, pages 123–137. Springer, 1992.

    Google Scholar 

  5. O. Burkart and B. Steffen. Composition, Decomposition and Model-Checking of Pushdown Processes. Nordic Journal of Computing, 2:89–125, 1995.

    Google Scholar 

  6. O. Burkart and B. Steffen. Model Checking the Full-Modal Mu-Calculus for Infinite Sequential Processes. Technical Report LFCS-97-355, University of Edinburgh, April 1997.

    Google Scholar 

  7. D. Caucal. On Infinite Transition Graphs Having a Decidable Monadic Theory. In ICALP '96, LNCS 1099, pages 194–205. Springer, 1996.

    Google Scholar 

  8. R. Cleaveland, M. Klein, and B. Steffen. Faster Model Checking for the Modal Mu-Calculus. In CAV '92, LNCS 663, pages 410–422, 1992.

    Google Scholar 

  9. B. Courcelle. Graph Rewriting: An Algebraic and Logic Approach. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, chapter 5, pages 193–242. Elsevier Science Publisher B.V., 1990.

    Google Scholar 

  10. H. Hungar and B. Steffen. Local Model-Checking for Context-Free Processes. Nordic Journal of Computing, 1(3):364–385, 1994.

    Google Scholar 

  11. D. Kozen. Results on the Propositional μ-Calculus. Theoretical Computer Science, 27:333–354, 1983.

    Article  Google Scholar 

  12. D.E. Long, A. Browne, E.M. Clarke, S. Jha, and W.R. Marrero. An Improved Algorithm for the Evaluation of Fixpoint Expressions. In CAV '94, LNCS 818, pages 338–350. Springer, 1994.

    Google Scholar 

  13. D.E. Muller and P.E. Schupp. The Theory of Ends, Pushdown Automata, and Second-Order Logic. Theoretical Computer Science, 37:51–75, 1985.

    Article  Google Scholar 

  14. R.O. Rabin. Decidability of Second-Order Theories and Automata on Infinite Trees. Transactions of the AMS, 141:1–35, 1969.

    Google Scholar 

  15. I. Walukiewicz. Pushdown Processes: Games and Model-Checking. In CAV '96, LNCS 1102. Springer, 1996.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Pierpaolo Degano Roberto Gorrieri Alberto Marchetti-Spaccamela

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Burkart, O., Steffen, B. (1997). Model checking the full modal mu-calculus for infinite sequential processes. In: Degano, P., Gorrieri, R., Marchetti-Spaccamela, A. (eds) Automata, Languages and Programming. ICALP 1997. Lecture Notes in Computer Science, vol 1256. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63165-8_198

Download citation

  • DOI: https://doi.org/10.1007/3-540-63165-8_198

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63165-1

  • Online ISBN: 978-3-540-69194-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics