Model-Equivalent Reductions

  • Xishun Zhao
  • Hans Kleine Büning
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3569)


In this paper, the notions of polynomial–time model equivalent reduction and polynomial–space model equivalent reduction are introduced in order to investigate in a subtle way the expressive power of different theories. We compare according to these notions some classes of propositional formulas and quantified Boolean formulas. Our results show that classes of theories with the same complexity might have different representation strength under some conjectures which are widely believed to be true in computation complexity theory.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Ben-Eliyahu, R., Dechter, R.: Default Logic, Propositional Logic and Constraints. In: Proceedings of the Ninth National Conference on Artificial Intelligence (AAAI 1991) (1991)Google Scholar
  2. 2.
    Cadoli, M., Donini, F.M., Schaerf, M.: Is Intractability of Nonmonotonic Reasoning a Real Drawback. Artificial intelligence 88(2), 215–251 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Clark, K.: Negation as failure. In: Gallaire, H., Minker, J. (eds.) Logic and Data Bases, pp. 293–322. Plenum Press, New YorkGoogle Scholar
  4. 4.
    Ebbinhaus, H.D., Flum, J.: Finite Model Theory. Springer, Heidelberg (1999)Google Scholar
  5. 5.
    Eiter, T., Gottlob, G.: On the Computational Cost of Disjunctive Logic Programming: Propositional Case. Annals of Mathematics and Artificial Intelligence 15, 289–323 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Fages, F.: Consistency of Clark’s Completion and Existence of Stable Models. Journal of Methods of Logic in Computer Science 1, 51–60 (1994)Google Scholar
  7. 7.
    Flögel, A.: Resolution für Quantifizierte Boole’sche Formeln, Disertation, Paderborn University (1993)Google Scholar
  8. 8.
    Greenlaw, R., Hoover, H.J., Ruzzo, W.L.: Limits to Parallep Computation: P-Completeness theory. Oxford University Press, Oxford (1995)Google Scholar
  9. 9.
    Gelfond, M., Lifschitz, V.: The Stable Model Semantics for Logic Programming. In: Proceedings of the 5th International Conference on Logic Programming, pp. 1070–1080. The MIT Press, Cambridge (1988)Google Scholar
  10. 10.
    Gelfond, M., Lifschitz, V.: Classical Negation in Logic Programs and Disjunctive Database. New Generation Computing 9, 365–385 (1991)CrossRefGoogle Scholar
  11. 11.
    Gogic, G., Kautz, H., Papadimitriou, C., Selman, B.: The Comparative Liguistics of Knowledge Representation. In: Proceedings of IJCAI 1995, Montreal, Canada (1995)Google Scholar
  12. 12.
    Karpinski, M., Kleine Büning, H., Schmitt, P.H.: On the Computational Complexity of Quantified Horn Clauses. In: Börger, E., Kleine Büning, H., Richter, M.M. (eds.) CSL 1987. LNCS, vol. 329, pp. 129–137. Springer, Heidelberg (1988)Google Scholar
  13. 13.
    Kleine Büning, H., Lettmann, T.: Propositional Logic: Deduction and Algorithms. Cambridge University Press, Cambridge (1999)zbMATHGoogle Scholar
  14. 14.
    Kleine Büning, H., Zhao, X.: Equivalence Models for Quantified Boolean Formulas. In: Hoos, H.H., Mitchell, D.G. (eds.) SAT 2004. LNCS, vol. 3542, pp. 224–234. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  15. 15.
    Johnson, D.S.: A Catalog of Complexity Classes. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science, vol. A, pp. 67–161. Elsevier Science Publisher (North-Holland), Amsterdam (1990)Google Scholar
  16. 16.
    Lee, J., Lin, F.: Loop Formulas for Circumscription. In: AAAI 2004, pp. 281–286 (2004)Google Scholar
  17. 17.
    Lee, J., Lifschitz, V.: Loop Formulas for Disjunctive Logic Programs. In: Palamidessi, C. (ed.) ICLP 2003. LNCS, vol. 2916, pp. 451–465. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  18. 18.
    Lifschitz, V., Razborov, A.: Why Are There So Many Loop Formulas (2003) (Manuscription)Google Scholar
  19. 19.
    Lifschitz, V., Pearce, D., Valverde, A.: Strongly Equivalent Logic Programs. ACM Transactions on Computational Logic 2, 526–541 (2001)CrossRefMathSciNetGoogle Scholar
  20. 20.
    Lin, F., Zhao, Y.: ASSAT: Computing Answer Sets of a Logic Program by SAT Solvers. Artifficial Intelligence 157, 115–137 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Konolige, K.: On the Relation between Default and Autoepistemic Logic. Artificial Intelligence 35(3), 343–382 (1988)zbMATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    Marek, W., Truszczyński, M.: Nonmonotonic Logic. Springer, Heidelberg (1993)zbMATHGoogle Scholar
  23. 23.
    Spira, P.M.: On Time Hardware Complexity Tradeoffs for Boolean Functions. In: Proceedings of the 4th Hawaii Symposium on System Science, Western Periodicals Company, North Hollywood, pp. 525–527 (1971)Google Scholar
  24. 24.
    Tseitin, G.S.: On the Complexity of Derivation in Propositional Calculus. In: Silenko, A.O. (ed.) Studies in Constructive Mathematics and Mathematical Logic, Part II, pp. 115–125 (1970)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Xishun Zhao
    • 1
  • Hans Kleine Büning
    • 2
  1. 1.Institute of Logic and CognitionSun Yat-sen UniversityGuangzhouP.R. China
  2. 2.Department of Computer ScienceUniversität PaderbornPaderbornGermany

Personalised recommendations