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Weakly-Synchronized Ground Tree Rewriting

(with Applications to Verifying Multithreaded Programs)

  • Conference paper
Mathematical Foundations of Computer Science 2012 (MFCS 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7464))

Abstract

Ground tree rewrite systems (GTRS) are a well-known treeextension of prefix-rewrite systems on words (a.k.a. pushdown systems), where subtrees (instead of word prefixes) are rewritten. GTRS can model programs with unbounded recursion depth and thread-spawning, wherein the threads have a tree-shaped dependency graph. We consider the extension of GTRS with a finite (global) control unit for synchronizing among the active threads, a.k.a. state-extended GTRS (sGTRS). Since sGTRS is Turing-complete, we restrict the finite control unit to dags possibly with self-loops, a.k.a. weakly-synchronized GTRS (wGTRS). wGTRS can be regarded as a generalization of context-bounded analysis of multipushdown systems with dynamic thread spawning. We show that reachability, repeated reachability, and the complement of model checking deterministic LTL over weakly-synchronized GTRS (wGTRS) are NP-complete by a polynomial reduction to checking existential Presburger formulas, for which highly optimized solvers are available.

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References

  1. Atig, M.F., Bollig, B., Habermehl, P.: Emptiness of Multi-pushdown Automata Is 2ETIME-Complete. In: Ito, M., Toyama, M. (eds.) DLT 2008. LNCS, vol. 5257, pp. 121–133. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  2. Atig, M.F., Bouajjani, A., Qadeer, S.: Context-bounded analysis for concurrent programs with dynamic creation of threads. LMCS 7(4) (2011)

    Google Scholar 

  3. Bouajjani, A., Müller-Olm, M., Touili, T.: Regular Symbolic Analysis of Dynamic Networks of Pushdown Systems. In: Abadi, M., de Alfaro, L. (eds.) CONCUR 2005. LNCS, vol. 3653, pp. 473–487. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  4. Bozzelli, L., Kretínský, M., Rehák, V., Strejcek, J.: On decidability of LTL model checking for process rewrite systems. Acta Inf. 46(1), 1–28 (2009)

    Article  MATH  Google Scholar 

  5. Burkart, O., Caucal, D., Moller, F., Steffen, B.: Verification on infinite structures. In: Handbook of Process Algebra, pp. 545–623. Elsevier, North-Holland (2001)

    Google Scholar 

  6. Comon, H., Dauchet, M., Gilleron, R., Löding, C., Jacquemard, F., Lugiez, D., Tison, S., Tommasi, M.: Tree automata techniques and applications (2007)

    Google Scholar 

  7. de Moura, L., Bjørner, N.S.: Z3: An Efficient SMT Solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337–340. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  8. Esparza, J., Ganty, P.: Complexity of pattern-based verification for multithreaded programs. In: POPL, pp. 499–510 (2011)

    Google Scholar 

  9. Fisler, K.: Toward diagrammability and efficiency in event-sequence languages. Int. J. Softw. Tools Technol. Transf. 8(4), 431–447 (2006)

    Article  Google Scholar 

  10. Ganty, P., Majumdar, R., Monmege, B.: Bounded underapproximations. Formal Methods in System Design 40(2), 206–231 (2012)

    Article  Google Scholar 

  11. Göller, S., Lin, A.W.: Refining the Process Rewrite Systems Hierarchy via Ground Tree Rewrite Systems. In: Katoen, J.-P., König, B. (eds.) CONCUR 2011 – Concurrency Theory. LNCS, vol. 6901, pp. 543–558. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  12. Kozen, D.C.: Automata and Computability. Springer (2007)

    Google Scholar 

  13. Křetínský, M., Řehák, V., Strejček, J.: Extended Process Rewrite Systems: Expressiveness and Reachability. In: Gardner, P., Yoshida, N. (eds.) CONCUR 2004. LNCS, vol. 3170, pp. 355–370. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  14. Löding, C.: Infinite Graphs Generated by Tree Rewriting. PhD thesis, RWTH Aachen (2003)

    Google Scholar 

  15. Madhusudan, P., Parlato, G.: The tree width of auxiliary storage. In: POPL, pp. 283–294 (2011)

    Google Scholar 

  16. Maidl, M.: The common fragment of CTL and LTL. In: FOCS, pp. 643–652 (2000)

    Google Scholar 

  17. Mayr, R.: Decidability and Complexity of Model Checking Problems for Infinite-State Systems. PhD thesis, TU-Munich (1998)

    Google Scholar 

  18. 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)

    Chapter  Google Scholar 

  19. Ramalingam, G.: Context-sensitive synchronization-sensitive analysis is undecidable. ACM Trans. Program. Lang. Syst. 22(2), 416–430 (2000)

    Article  Google Scholar 

  20. Scarpellini, B.: Complexity of subcases of presburger arithmetic. Trans. of AMS 284(1), 203–218 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  21. To, A.W.: Model Checking Infinite-State Systems: Generic and Specific Approaches. PhD thesis, LFCS, School of Informatics, University of Edinburgh (2010)

    Google Scholar 

  22. Torre, S.L., Madhusudan, P., Parlato, G.: A robust class of context-sensitive languages. In: LICS, pp. 161–170 (2007)

    Google Scholar 

  23. Vardi, M.Y., Wolper, P.: An automata-theoretic approach to automatic program verification (preliminary report). In: LICS, pp. 332–344 (1986)

    Google Scholar 

  24. Verma, K.N., Seidl, H., Schwentick, T.: On the Complexity of Equational Horn Clauses. In: Nieuwenhuis, R. (ed.) CADE 2005. LNCS (LNAI), vol. 3632, pp. 337–352. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, Oxford University, UK

    Anthony Widjaja Lin

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  1. Anthony Widjaja Lin
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Comenius University, Mlynska Dolina, 84248, Bratislava, Slovakia

    Branislav Rovan

  2. Department of Electronics and Computer Science, University of Southampton, SO17 1BJ, Southampton, UK

    Vladimiro Sassone

  3. Institute of Theoretical Computer Science, ETH Zürich, CAB H 39.2, Universitätstrasse 6, 8092, Zürich, Switzerland

    Peter Widmayer

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Lin, A.W. (2012). Weakly-Synchronized Ground Tree Rewriting. In: Rovan, B., Sassone, V., Widmayer, P. (eds) Mathematical Foundations of Computer Science 2012. MFCS 2012. Lecture Notes in Computer Science, vol 7464. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32589-2_55

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  • DOI: https://doi.org/10.1007/978-3-642-32589-2_55

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-32588-5

  • Online ISBN: 978-3-642-32589-2

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