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International Conference on Theory and Applications of Satisfiability Testing

SAT 2012: Theory and Applications of Satisfiability Testing – SAT 2012 pp 157–171Cite as

Generalized Property Directed Reachability

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7317))

Abstract

The IC3 algorithm was recently introduced for proving properties of finite state reactive systems. It has been applied very successfully to hardware model checking. We provide a specification of the algorithm using an abstract transition system and highlight its dual operation: model search and conflict resolution. We then generalize it along two dimensions. Along one dimension we address nonlinear fixed-point operators (push-down systems) and evaluate the algorithm on Boolean programs. In the second dimension we leverage proofs and models and generalize the method to Boolean constraints involving theories.

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References

  1. Albarghouthi, A., Gurfinkel, A., Chechik, M.: Whale: An Interpolation-Based Algorithm for Inter-procedural Verification. In: Kuncak, V., Rybalchenko, A. (eds.) VMCAI 2012. LNCS, vol. 7148, pp. 39–55. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  2. Ball, T., Rajamani, S.K.: The SLAM project: debugging system software via static analysis. SIGPLAN Not. 37(1), 1–3 (2002)

    Article  Google Scholar 

  3. Blass, A., Gurevich, Y.: Existential Fixed-Point Logic. In: Börger, E. (ed.) Computation Theory and Logic. LNCS, vol. 270, pp. 20–36. Springer, Heidelberg (1987)

    Chapter  Google Scholar 

  4. Bradley, A.R.: SAT-Based Model Checking without Unrolling. In: Jhala, R., Schmidt, D. (eds.) VMCAI 2011. LNCS, vol. 6538, pp. 70–87. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  5. Clarke, E.M., Grumberg, O., Jha, S., Lu, Y., Veith, H.: Counterexample-guided abstraction refinement. Journal of the ACM 50(5), 752–794 (2003)

    Article  MathSciNet  Google Scholar 

  6. Een, N., Mishchenko, A., Brayton, R.: Efficient implementation of property-directed reachability. In: FMCAD (2011)

    Google Scholar 

  7. Grebenshchikov, S., Lopes, N.P., Popeea, C., Rybalchenko, A.: Synthesizing software verifiers from proof rules. In: PLDI (2012)

    Google Scholar 

  8. Gupta, A., Popeea, C., Rybalchenko, A.: Solving Recursion-Free Horn Clauses over LI+UIF. In: Yang, H. (ed.) APLAS 2011. LNCS, vol. 7078, pp. 188–203. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  9. Hoder, K., Bjørner, N., de Moura, L.: μZ– An Efficient Engine for Fixed Points with Constraints. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 457–462. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  10. Liffiton, M.H., Sakallah, K.A.: Algorithms for computing minimal unsatisfiable subsets of constraints. J. Autom. Reasoning 40(1), 1–33 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  11. Manna, Z., Pnueli, A.: Temporal verification of reactive systems - safety (1995)

    Google Scholar 

  12. McMillan, K.L.: Interpolants from Z3 proofs. In: FMCAD (2011)

    Google Scholar 

  13. Nieuwenhuis, R., Oliveras, A., Tinelli, C.: Solving SAT and SAT Modulo Theories: From an abstract DPLL procedure to DPLL(T). J. ACM 53(6) (2006)

    Google Scholar 

  14. Revesz, P.Z.: Safe Datalog Queries with Linear Constraints. In: Maher, M.J., Puget, J.-F. (eds.) CP 1998. LNCS, vol. 1520, pp. 355–369. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. The University of Manchester, UK

    Kryštof Hoder

  2. Microsoft Research, Redmond, USA

    Nikolaj Bjørner

Authors
  1. Kryštof Hoder
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  2. Nikolaj Bjørner
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Editor information

Editors and Affiliations

  1. Center for Information Technology, Fondazione Bruno Kessler, via Sommarive 18, Povo, 38123, Trento, Italy

    Alessandro Cimatti

  2. Department of Information Engineering and Computer Science, University of Trento, via Sommarive 14, Povo, 38123, Trento, Italy

    Roberto Sebastiani

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© 2012 Springer-Verlag Berlin Heidelberg

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Hoder, K., Bjørner, N. (2012). Generalized Property Directed Reachability. In: Cimatti, A., Sebastiani, R. (eds) Theory and Applications of Satisfiability Testing – SAT 2012. SAT 2012. Lecture Notes in Computer Science, vol 7317. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31612-8_13

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  • DOI: https://doi.org/10.1007/978-3-642-31612-8_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31611-1

  • Online ISBN: 978-3-642-31612-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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