Generalized Property Directed Reachability

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7317)


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.


Transition Relation Safety Property Horn Clause Predicate Transformer Uninterpreted Function 
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.
    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)CrossRefGoogle Scholar
  2. 2.
    Ball, T., Rajamani, S.K.: The SLAM project: debugging system software via static analysis. SIGPLAN Not. 37(1), 1–3 (2002)CrossRefGoogle Scholar
  3. 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)CrossRefGoogle Scholar
  4. 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)CrossRefGoogle Scholar
  5. 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)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Een, N., Mishchenko, A., Brayton, R.: Efficient implementation of property-directed reachability. In: FMCAD (2011)Google Scholar
  7. 7.
    Grebenshchikov, S., Lopes, N.P., Popeea, C., Rybalchenko, A.: Synthesizing software verifiers from proof rules. In: PLDI (2012)Google Scholar
  8. 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)CrossRefGoogle Scholar
  9. 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)CrossRefGoogle Scholar
  10. 10.
    Liffiton, M.H., Sakallah, K.A.: Algorithms for computing minimal unsatisfiable subsets of constraints. J. Autom. Reasoning 40(1), 1–33 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Manna, Z., Pnueli, A.: Temporal verification of reactive systems - safety (1995)Google Scholar
  12. 12.
    McMillan, K.L.: Interpolants from Z3 proofs. In: FMCAD (2011)Google Scholar
  13. 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. 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)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.The University of ManchesterUK
  2. 2.Microsoft ResearchRedmondUSA

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