Mapping Conformant Planning into SAT Through Compilation and Projection

  • Héctor Palacios
  • Héctor Geffner
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4177)


Conformant planning is a variation of classical AI planning where the initial state is partially known and actions can have non-deterministic effects. While a classical plan must achieve the goal from a given initial state using deterministic actions, a conformant plan must achieve the goal in the presence of uncertainty in the initial state and action effects. Conformant planning is computationally harder than classical planning, and unlike classical planning, cannot be reduced polynomially to SAT (unless P = NP). Current SAT approaches to conformant planning, such as those considered by Giunchiglia and colleagues, thus follow a generate-and-test strategy: the models of the theory are generated one by one using a SAT solver (assuming a given planning horizon), and from each such model, a candidate conformant plan is extracted and tested for validity using another SAT call. This works well when the theory has few candidate plans and models, but otherwise is too inefficient. In this paper we propose a different use of a SAT engine where conformant plans are computed by means of a single SAT call over a transformed theory. This transformed theory is obtained by projecting the original theory over the action variables. This operation, while intractable, can be done efficiently provided that the original theory is compiled into d–DNNF (Darwiche 2001), a form akin to OBDDs (Bryant 1992). The experiments that are reported show that the resulting compile-project-sat planner is competitive with state-of-the-art optimal conformant planners and improves upon a planner recently reported at ICAPS-05.


Model Check Planning Horizon Belief Space Classical Planning Conformant Planning 
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.
    Ferraris, P., Giunchiglia, E.: Planning as satisfiability in nondeterministic domains. In: Proceedings AAAI-2000, pp. 748–753 (2000)Google Scholar
  2. 2.
    Darwiche, A., Marquis, P.: A knowledge compilation map. Journal of Artificial Intelligence Research 17, 229–264 (2002)MATHMathSciNetGoogle Scholar
  3. 3.
    Bryant, R.E.: Symbolic Boolean manipulation with ordered binary-decision diagrams. ACM Computing Surveys 24, 293–318 (1992)CrossRefGoogle Scholar
  4. 4.
    Palacios, H., Bonet, B., Darwiche, A., Geffner, H.: Pruning conformant plans by counting models on compiled d-DNNF representations. In: Proc. of the 15th Int. Conf. on Planning and Scheduling (ICAPS 2005), pp. 141–150. AAAI Press, Menlo Park (2005)Google Scholar
  5. 5.
    Rintanen, J.: Distance estimates for planning in the discrete belief space. In: Proc. AAAI 2004, pp. 525–530 (2004)Google Scholar
  6. 6.
    Kautz, H., Selman, B.: Pushing the envelope: Planning, propositional logic, and stochastic search. In: Proceedings of AAAI 1996, pp. 1194–1201 (1996)Google Scholar
  7. 7.
    Lin, F., Reiter, R.: Forget it! In: Working Notes. In: AAAI Fall Symposium on Relevance, American Association for Artificial Intelligence, pp. 154–159 (1994)Google Scholar
  8. 8.
    Giunchiglia, F., Traverso, P.: Planning as model checking. In: Biundo, S., Fox, M. (eds.) ECP 1999. LNCS, vol. 1809, Springer, Heidelberg (2000)CrossRefGoogle Scholar
  9. 9.
    Clarke, E., Grumberg, O., Peled, D.: Model Checking. MIT Press, Cambridge (2000)Google Scholar
  10. 10.
    Cimatti, A., Roveri, M.: Conformant planning via symbolic model checking. Journal of Artificial Intelligence Research 13, 305–338 (2000)MATHGoogle Scholar
  11. 11.
    Darwiche, A.: On the tractable counting of theory models and its applications to belief revision and truth maintenance. J. of Applied Non-Classical Logics (2002)Google Scholar
  12. 12.
    Darwiche, A.: New advances in compiling cnf into decomposable negation normal form. In: Proc. ECAI 2004, pp. 328–332 (2004)Google Scholar
  13. 13.
    Brafman, R., Hoffmann, J.: Conformant planning via heuristic forward search: A new approach. In: Proceedings of the 14th International Conference on Automated Planning and Scheduling, ICAPS 2004 (2004)Google Scholar
  14. 14.
    Rintanen, J.: Constructing conditional plans by a theorem-prover. Journal of Artificial Intelligence Research 10, 323–352 (1999)MATHGoogle Scholar
  15. 15.
    Biere, A.: Resolve and expand. In: Hoos, H., Mitchell, D.G. (eds.) SAT 2004. LNCS, vol. 3542, pp. 59–70. Springer, Heidelberg (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Héctor Palacios
    • 1
  • Héctor Geffner
    • 2
  1. 1.Universitat Pompeu FabraBarcelonaSpain
  2. 2.ICREA & Universitat Pompeu FabraBarcelonaSpain

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