Temporal Logics for Concurrent Recursive Programs: Satisfiability and Model Checking

  • Benedikt Bollig
  • Aiswarya Cyriac
  • Paul Gastin
  • Marc Zeitoun
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6907)


We develop a general framework for the design of temporal logics for concurrent recursive programs. A program execution is modeled as a partial order with multiple nesting relations. To specify properties of executions, we consider any temporal logic whose modalities are definable in monadic second-order logic and that, in addition, allows PDL-like path expressions. This captures, in a unifying framework, a wide range of logics defined for ranked and unranked trees, nested words, and Mazurkiewicz traces that have been studied separately. We show that satisfiability and model checking are decidable in EXPTIME and 2EXPTIME, depending on the precise path modalities.


Model Check Binary Tree Temporal Logic Path Expression Phase Switch 
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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  1. 1.
    Alur, R., Arenas, M., Barceló, P., Etessami, K., Immerman, N., Libkin, L.: First-order and temporal logics for nested words. Log. Meth. Comput. Sci. 4(4) (2008)Google Scholar
  2. 2.
    Alur, R., Etessami, K., Madhusudan, P.: A temporal logic of nested calls and returns. In: Jensen, K., Podelski, A. (eds.) TACAS 2004. LNCS, vol. 2988, pp. 467–481. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  3. 3.
    Alur, R., Madhusudan, P.: Adding nesting structure to words. Journal of the ACM 56, 16:1–16:43 (2009)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Atig, M.F.: Global Model Checking of Ordered Multi-Pushdown Systems. In: FSTTCS 2010, vol. 8, pp. 216–227 (2010)Google Scholar
  5. 5.
    Bollig, B., Grindei, M.-L., Habermehl, P.: Realizability of concurrent recursive programs. In: de Alfaro, L. (ed.) FOSSACS 2009. LNCS, vol. 5504, pp. 410–424. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  6. 6.
    Calvanese, D., De Giacomo, G., Lenzerini, M., Vardi, M.Y.: An Automata-Theoretic Approach to Regular XPath. In: Gardner, P., Geerts, F. (eds.) DBPL 2009. LNCS, vol. 5708, pp. 18–35. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  7. 7.
    Clarke, E.M., Emerson, E.A.: Design and synthesis of synchronization skeletons using branching-time temporal logic. In: Logic of Programs, pp. 52–71 (1981)Google Scholar
  8. 8.
    Dax, C., Klaedtke, F.: Alternation elimination for automata over nested words. In: Hofmann, M. (ed.) FOSSACS 2011. LNCS, vol. 6604, pp. 168–183. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  9. 9.
    Diekert, V., Gastin, P.: Pure future local temporal logics are expressively complete for Mazurkiewicz traces. Information and Computation 204(11), 1597–1619 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Diekert, V., Rozenberg, G. (eds.): The Book of Traces. World Scientific, Singapore (1995)Google Scholar
  11. 11.
    Fischer, M.J., Ladner, R.E.: Propositional dynamic logic of regular programs. Journal of Computer and System Sciences 18(2), 194–211 (1979)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Gastin, P., Kuske, D.: Satisfiability and model checking for MSO-definable temporal logics are in PSPACE. In: Amadio, R.M., Lugiez, D. (eds.) CONCUR 2003. LNCS, vol. 2761, pp. 222–236. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  13. 13.
    Gastin, P., Kuske, D.: Uniform satisfiability problem for local temporal logics over Mazurkiewicz traces. Information and Computation 208(7), 797–816 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Göller, S., Lohrey, M., Lutz, C.: PDL with intersection and converse: satisfiability and infinite-state model checking. J. Symb. Log. 74(1), 279–314 (2009)zbMATHCrossRefGoogle Scholar
  15. 15.
    La Torre, S., Madhusudan, P., Parlato, G.: A robust class of context-sensitive languages. In: LICS 2007, pp. 161–170. IEEE Computer Society Press, Los Alamitos (2007)Google Scholar
  16. 16.
    Lange, M., Lutz, C.: 2-ExpTime lower bounds for Propositional Dynamic Logics with Intersection. J. Symb. Log. 70(5), 1072–1086 (2005)MathSciNetzbMATHGoogle Scholar
  17. 17.
    Libkin, L.: Logics for Unranked Trees: An Overview. Log. Meth. Comput. Sci. 2(3) (2006)Google Scholar
  18. 18.
    Pnueli, A.: The temporal logic of programs. In: Proceedings of FOCS 1977, pp. 46–57. IEEE, Los Alamitos (1977)Google Scholar
  19. 19.
    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)CrossRefGoogle Scholar
  20. 20.
    Vardi, M.Y.: The taming of converse: Reasoning about two-way computations. In: Parikh, R. (ed.) Logic of Programs 1985. LNCS, vol. 193, pp. 413–423. Springer, Heidelberg (1985)Google Scholar
  21. 21.
    Vardi, M.Y.: Reasoning about the past with two-way automata. In: Larsen, K.G., Skyum, S., Winskel, G. (eds.) ICALP 1998. LNCS, vol. 1443, pp. 628–641. Springer, Heidelberg (1998)CrossRefGoogle Scholar

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© Springer-Verlag GmbH Berlin Heidelberg 2011

Authors and Affiliations

  • Benedikt Bollig
    • 1
  • Aiswarya Cyriac
    • 1
  • Paul Gastin
    • 1
  • Marc Zeitoun
    • 1
  1. 1.LSV, ENS Cachan, CNRS & INRIAFrance

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