Generalized Model-Checking Problems for First-Order Logic

  • Martin Grohe
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2010)

Abstract

Descriptive complexity theory provides a convenient and intuitive way to model a large variety of computational problems. The basic problem studied in descriptive complexity is of the following form:

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References

  1. 1.
    A.V. Aho, J.E. Hopcroft, and J.D. Ullman. The Design and Analysis of Computer Algorithms. Addison-Wesley, 1974.Google Scholar
  2. 2.
    S. Arnborg, J. Lagergren, and D. Seese. Easy problems for tree-decomposable graphs. Journal of Algorithms, 12:308–340, 1991.MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    A. Chandra and D. Harel. Structure and complexity of relational queries. Journal of Computer and System Sciences, 25:99–128, 1982.MATHCrossRefGoogle Scholar
  4. 4.
    A.K. Chandra and P.M. Merlin. Optimal implementation of conjunctive queries in relational data bases. In Proceedings of the 9th ACM Symposium on Theory of Computing, pages 77–90, 1977.Google Scholar
  5. 5.
    Ch. Chekuri and A. Rajaraman. Conjunctive query containment revisited. In Ph. Kolaitis and F. Afrati, editors, Proceedings of the 5th International Conference on Database Theory, volume 1186 of Lecture Notes in Computer Science, pages 56–70. Springer-Verlag, 1997.Google Scholar
  6. 6.
    J.H. Conway and C.McA. Gordon. Knots and links in spatial graphs. Journal of Graph Theory, 7:445–453, 1983.MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    B. Courcelle. Graph rewriting: An algebraic and logic approach. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, volume 2, pages 194–242. Elsevier Science Publishers, 1990.Google Scholar
  8. 8.
    R. Diestel. Graph Theory. Springer-Verlag, second edition, 2000.Google Scholar
  9. 9.
    R.G. Downey and M.R. Fellows. Parameterized Complexity. Springer-Verlag, 1999.Google Scholar
  10. 10.
    R.G. Downey, M.R. Fellows, and U. Taylor. The parameterized complexity of relational database queries and an improved characterization of W[1]. In Bridges, Calude, Gibbons, Reeves, and Witten, editors, Combinatorics, Complexity, and Logic-Proceedings of DMTCS’ 96, pages 194–213. Springer-Verlag, 1996.Google Scholar
  11. 11.
    T. Feder and M.Y. Vardi. Monotone monadic SNP and constraint satisfaction. In Proceedings of the 25th ACM Symposium on Theory of Computing, pages 612–622, 1993.Google Scholar
  12. 12.
    J. Flum, M. Frick, and M. Grohe. Query evaluation via tree-decompositions. In Jan van den Bussche and Victor Vianu, editors, Proceedings of the 8th International Conference on Database Theory, Lecture Notes in Computer Science. Springer Verlag, 2001. To appear.Google Scholar
  13. 13.
    J. Flum and M. Grohe. Fixed-parameter tractability and logic. Submitted for publication.Google Scholar
  14. 14.
    M. Frick. Easy Instances for Model Checking. PhD thesis, Albert-Ludwigs-Universität Freiburg. To appear.Google Scholar
  15. 15.
    M. Frick and M. Grohe. Deciding first-order properties of locally tree-decomposable structures. Submitted for publication. A preliminary version of the paper appeared in Proceedings of the 26th International Colloquium on Automata, Languages and Programming, LNCS 1644, Springer-Verlag, 1999.CrossRefGoogle Scholar
  16. 16.
    H. Gaifman. On local and non-local properties. In Proceedings of the Herbrand Symposium, Logic Colloquium’ 81. North Holland, 1982.Google Scholar
  17. 17.
    M.R. Garey and D.S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, 1979.Google Scholar
  18. 18.
    L.A. Goldberg. Efficient Algorithms for Listing Combinatorial Structures. Cambridge Uni-versity Press, 1993.Google Scholar
  19. 19.
    G. Gottlob, N. Leone, and F. Scarcello. A comparison of structural CSP decomposition methods. In Thomas Dean, editor, Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence, pages 394–399. Morgan Kaufmann, 1999.Google Scholar
  20. 20.
    G. Gottlob, N. Leone, and F. Scarcello. Hypertree decompositions and tractable queries. In Proceedings of the 18th ACM Symposium on Principles of Database Systems, pages 21–32, 1999.Google Scholar
  21. 21.
    M. Grohe. The complexity of generalized model-checking problems. In preparation.Google Scholar
  22. 22.
    M. Grohe, T. Schwentick, and L. Segoufin. When is the evaluation of conjunctive queries tractable, 2000. Submitted for publication.Google Scholar
  23. 23.
    M.R. Jerrum, L.G. Valiant, and V.V. Vazirani. Random generation of combinatorial structures from a uniform distribution. Theoretical Computer Science, 43:16–188, 1986.CrossRefMathSciNetGoogle Scholar
  24. 24.
    D.S. Johnson, C.H. Papadimitriou, and M. Yannakakis. On generating all maximal indepen-dent sets. Information Processing Letters, 27:119–123, 1988.MATHCrossRefMathSciNetGoogle Scholar
  25. 25.
    Ph.G. Kolaitis and M.Y. Vardi. Conjunctive-query containment and constraint satisfaction. In Proceedings of the 17th ACM Symposium on Principles of Database Systems, pages 205–213, 1998.Google Scholar
  26. 26.
    C.H. Papadimitriou and M. Yannakakis. On the complexity of database queries. In Proceedings of the 17th ACM Symposium on Principles of Database Systems, pages 12–19, 1997.Google Scholar
  27. 27.
    D. Seese. Linear time computable problems and first-order descriptions. Mathematical Structures in Computer Science, 6:505–526, 1996.MATHMathSciNetGoogle Scholar
  28. 28.
    L.J. Stockmeyer. The Complexity of Decision Problems in Automata Theory. PhD thesis, Department of Electrical Engineering, MIT, 1974.Google Scholar
  29. 29.
    L.G. Valiant. The complexity of combinatorial computations: An introduction. In GI 8. Jahrestagung Informatik, Fachberichte 18, pages 326–337, 1978.Google Scholar
  30. 30.
    P. van Emde Boas. Machine models and simulations. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, volume 1, pages 1–66. Elsevier Science Publishers, 1990.Google Scholar
  31. 31.
    M.Y. Vardi. The complexity of relational query languages. In Proceedings of the 14th ACM Symposium on Theory of Computing, pages 137–46, 1982.Google Scholar
  32. 32.
    M.Y. Vardi. Constraint satisfaction and database theory: A tutorial. In Proceedings of the 19th ACM Symposium on Principles of Database Systems, pages 76–85, 2000.Google Scholar
  33. 33.
    M. Yannakakis. Algorithms for acyclic database schemes. In 7th International Conference on Very Large Data Bases, pages 82–94, 1981.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Martin Grohe
    • 1
  1. 1.Department of Mathematics, Statistics, and Computer ScienceUICChicagoUSA

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