Some Results on the Complexity of Planning with Incomplete Information

  • Patrik Haslum
  • Peter Jonsson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1809)

Abstract

Planning with incomplete information may mean a number of different things; that certain facts of the initial state are not known, that operators can have random or nondeterministic effects, or that the plans created contain sensing operations and are branching. Study of the complexity of incomplete information planning has so far been concentrated on probabilistic domains, where a number of results have been found. We examine the complexity of planning in nondeterministic propositional domains. This differs from domains involving randomness, which has been well studied, in that for a nondeterministic choice, not even a probability distribution over the possible outcomes is known. The main result of this paper is that the non-branching plan existence problem in unobservable domains with an expressive operator formalism is EXPSPACE-complete. We also discuss several restrictions, which bring the complexity of the problem down to PSPACE-complete, and extensions to the fully and partially observable cases.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Baral, C., Kreinovich, V., Trejo, R.: Computational complexity of planning and approximate planning in presence of incompleteness. In: Proc. 16th International Joint Conference on Artificial Intelligence, IJCAI 1999 (1999)Google Scholar
  2. 2.
    Bylander, T.: Complexity results for planning. In: Proc. 12th International Joint Conference on Artificial Intelligence (1991)Google Scholar
  3. 3.
    Collins, G., Pryor, L.: Planning under uncertanity: Some key issues. In: Proc. 14th International Joint Conference on Artificial Intelligence (1995)Google Scholar
  4. 4.
    Draper, D., Hanks, S., Weld, D.: Probabilistic planning with information gathering and contingent execution. In: Artificial Intelligence Planning Systems: Proc. 2nd International Conference (1994)Google Scholar
  5. 5.
    Erol, K., Nau, D.S., Subrahmanian, V.S.: Complexity, decidability and undecidability results for domain-independent planning: A detailed analysis. Technical Report CS-TR-2797, Computer Science Department, University of Maryland (1991)Google Scholar
  6. 6.
    Goldsmith, J., Lusena, C., Mundhenk, M.: The complexity of deterministically observable finite-horizon markov decision processes. Technical Report 268-96, Computer Science Department, University of Kentucky (1996)Google Scholar
  7. 7.
    Hopcroft, J.E., Ullman, J.D.: Introduction to Automata theory, Languages and Computation. Addison-Wesley, Reading (1979)MATHGoogle Scholar
  8. 8.
    Johnson, D.S.: A catalog of complexity classes. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science, vol. A. Elsevier, Amsterdam (1990)Google Scholar
  9. 9.
    Kushmerick, N., Hanks, S., Weld, D.: An algorithm for probabilistic least- commitment planning. In: Proc. 12th National Conference on Artificial Intelligence (1994)Google Scholar
  10. 10.
    Littman, M.L.: Probabilistic propositional planning: Representations and complexity. In: Proc. 14th National Conference on Artificial Intelligence (1997)Google Scholar
  11. 11.
    Papadimitrou, C.H.: Computational Complexity. Addison-Wesley, Reading (1994)Google Scholar
  12. 12.
    Peot, M., Smith, D.: Conditional nonlinear planning. In: Artificial Intelligence Planning Systems: Proc. International Confrence (1992)Google Scholar
  13. 13.
    Warren, D.H.D.: Generating conditional plans and programs. In: Proceedings of the Summer Conference on AI and Simulation of Behaviour (1976)Google Scholar
  14. 14.
    Weld, D., Anderson, C., Smith, D.: Extending Graphplan to handle uncertainty & sensing actions. In: Proc. 15th National Conference on Artifical Intelligence, AAAI 1998 (1998)Google Scholar
  15. 15.
    Weld, D., Smith, D.: Conformant Graphplan. In: Proc. 15th National Conference on Artifical Intelligence, AAAI 1998 (1998)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Patrik Haslum
    • 1
  • Peter Jonsson
    • 1
  1. 1.Department of Computer and Information ScienceLinköping UniversityLinköpingSweden

Personalised recommendations