The recently introduced model checking algorithm, IC3, has proved to be among the best SAT-based safety model checkers. Many implementations now exist. This paper provides the context from which IC3 was developed and explains how the originator of the algorithm understands it. Then it draws parallels between IC3 and the subsequently developed algorithms, FAIR and IICTL, which extend IC3’s ideas to the analysis of ω-regular and CTL properties, respectively. Finally, it draws attention to certain challenges that these algorithms pose for the SAT and SMT community.


Model Check Linear Inequality Transition Relation Proof Obligation Abstract Domain 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Biere, A., Cimatti, A., Clarke, E., Zhu, Y.: Symbolic Model Checking without BDDs. In: Cleaveland, W.R. (ed.) TACAS 1999. LNCS, vol. 1579, pp. 193–207. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  2. 2.
    Bradley, A.R.: k-step relative inductive generalization. Technical report, CU Boulder (March 2010),
  3. 3.
    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
  4. 4.
    Bradley, A.R., Manna, Z.: Checking safety by inductive generalization of counterexamples to induction. In: FMCAD (November 2007)Google Scholar
  5. 5.
    Bradley, A.R., Manna, Z.: Verification Constraint Problems with Strengthening. In: Barkaoui, K., Cavalcanti, A., Cerone, A. (eds.) ICTAC 2006. LNCS, vol. 4281, pp. 35–49. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  6. 6.
    Bradley, A.R., Somenzi, F., Hassan, Z., Zhang, Y.: An incremental approach to model checking progress properties. In: FMCAD (November 2011)Google Scholar
  7. 7.
    Colón, M.A., Sankaranarayanan, S., Sipma, H.B.: Linear Invariant Generation Using Non-linear Constraint Solving. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 420–432. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  8. 8.
    Cousot, P., Cousot, R.: Abstract interpretation: A unified lattice model for static analysis of programs by construction or approximation of fixpoints. In: POPL (1977)Google Scholar
  9. 9.
    Cousot, P., Halbwachs, N.: Automatic discovery of linear restraints among variables of a program. In: POPL (January 1978)Google Scholar
  10. 10.
    Graf, S., Saidi, H.: Construction of Abstract state Graphs with PVS. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol. 1254, pp. 73–83. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  11. 11.
    Hassan, Z., Bradley, A.R., Somenzi, F.: Incremental, inductive CTL model checking. In: CAV (July 2012)Google Scholar
  12. 12.
    Lu, F., Iyer, M.K., Parthasarathy, G., Wang, L.-C., Cheng, K.-T., Chen, K.C.: An Efficient Sequential SAT Solver With Improved Search Strategies. In: DATE (2005)Google Scholar
  13. 13.
    Manna, Z., Pnueli, A.: Temporal Verification of Reactive Systems: Safety. Springer, New York (1995)CrossRefGoogle Scholar
  14. 14.
    McMillan, K.L.: Applying SAT Methods in Unbounded Symbolic Model Checking. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 250–264. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  15. 15.
    McMillan, K.L.: Interpolation and SAT-Based Model Checking. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 1–13. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  16. 16.
    McMillan, K.L.: Symbolic Model Checking. Kluwer, Boston (1994)Google Scholar
  17. 17.
    Sankaranarayanan, S., Sipma, H.B., Manna, Z.: Scalable Analysis of Linear Systems Using Mathematical Programming. In: Cousot, R. (ed.) VMCAI 2005. LNCS, vol. 3385, pp. 25–41. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  18. 18.
    Sheeran, M., Singh, S., Stålmarck, G.: Checking Safety Properties Using Induction and a SAT-Solver. In: Johnson, S.D., Hunt Jr., W.A. (eds.) FMCAD 2000. LNCS, vol. 1954, pp. 108–125. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  19. 19.
    Somenzi, F., Bradley, A.R.: IC3: Where monolithic and incremental meet. In: FMCAD (November 2011)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Aaron R. Bradley
    • 1
  1. 1.ECEE DepartmentUniversity of Colorado at BoulderUSA

Personalised recommendations