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Fixed-Point Definability and Polynomial Time

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Computer Science Logic (CSL 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5771))

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Abstract

My talk will be a survey of recent results about the quest for a logic capturing polynomial time.

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References

  1. Blass, A., Gurevich, Y., Shelah, S.: Choiceless polynomial time. Annals of Pure and Applied Logic 100, 141–187 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  2. Blass, A., Gurevich, Y., Shelah, S.: On polynomial time computation over unordered structures. Journal of Symbolic Logic 67, 1093–1125 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  3. Cai, J., Fürer, M., Immerman, N.: An optimal lower bound on the number of variables for graph identification. Combinatorica 12, 389–410 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  4. Chandra, A., Harel, D.: Structure and complexity of relational queries. Journal of Computer and System Sciences 25, 99–128 (1982)

    Article  MATH  Google Scholar 

  5. Chen, Y., Flum, J.: A logic for PTIME and a parameterized halting problem. In: Proceedings of the 24th IEEE Symposium on Logic in Computer Science (2009)

    Google Scholar 

  6. Dawar, A.: Generalized quantifiers and logical reducibilities. Journal of Logic and Computation 5, 213–226 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  7. Dawar, A., Grohe, M., Holm, B., Laubner, B.: Logics with rank operators. In: Proceedings of the 24th IEEE Symposium on Logic in Computer Science (2009)

    Google Scholar 

  8. Dawar, A., Richerby, D., Rossman, B.: Choiceless polynomial time, counting and the Cai-Fürer-Immerman graphs (Extended abstract). Electronic Notes on Theoretical Compututer Science 143, 13–26 (2006)

    Article  MATH  Google Scholar 

  9. Fagin, R.: Generalized first–order spectra and polynomial–time recognizable sets. In: Karp, R.M. (ed.) Complexity of Computation, SIAM-AMS Proceedings, vol. 7, pp. 43–73 (1974)

    Google Scholar 

  10. Grädel, E.: Finite Model Theory and Descriptive Complexity. In: Kolaitis, P.G., Libkin, L., Marx, M., Spencer, J., Vardi, M.Y., Venema, Y., Weinstein, S. (eds.) Finite Model Theory and Its Applications, ch. 3, pp. 125–230. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  11. Grohe, M.: Fixed-point logics on planar graphs. In: Proceedings of the 13th IEEE Symposium on Logic in Computer Science, pp. 6–15 (1998)

    Google Scholar 

  12. Grohe, M.: Definable tree decompositions. In: Proceedings of the 23rd IEEE Symposium on Logic in Computer Science, pp. 406–417 (2008)

    Google Scholar 

  13. Grohe, M., Ebbinghaus, H.-D.: Zur Struktur dessen, was wirklich berechenbar ist. Philosophia Naturalis 36, 91–116 (1999)

    MathSciNet  Google Scholar 

  14. Grohe, M., Mariño, J.: Definability and descriptive complexity on databases of bounded tree-width. In: Beeri, C., Bruneman, P. (eds.) ICDT 1999. LNCS, vol. 1540, pp. 70–82. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  15. Gurevich, Y.: Logic and the challenge of computer science. In: Börger, E. (ed.) Current trends in theoretical computer science, pp. 1–57. Computer Science Press, Rockville (1988)

    Google Scholar 

  16. Hella, L.: Definability hierarchies of generalized quantifiers. Annals of Pure and Applied Logic 43, 235–271 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  17. Hella, L., Kolaitis, P.G., Luosto, K.: Almost everywhere equivalence of logics in finite model theory. Bulletin of Symbolic Logic 2, 422–443 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  18. Immerman, N.: Upper and lower bounds for first-order expressibility. Journal of Computer and System Sciences 25, 76–98 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  19. Immerman, N.: Expressibility as a complexity measure: results and directions. In: Proceedings of the 2nd IEEE Symposium on Structure in Complexity Theory, pp. 194–202 (1987)

    Google Scholar 

  20. Immerman, N., Lander, E.: Describing graphs: A first-order approach to graph canonization. In: Selman, A. (ed.) Complexity theory retrospective, pp. 59–81. Springer, Heidelberg (1990)

    Chapter  Google Scholar 

  21. Nash, A., Remmel, J.B., Vianu, V.: PTIME queries revisited. In: Eiter, T., Libkin, L. (eds.) ICDT 2005. LNCS, vol. 3363, pp. 274–288. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  22. Otto, M.: Bisimulation-invariant PTIME and higher-dimensional μ-calculus. Theoretical Computer Science 224, 237–265 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  23. Vardi, M.Y.: The complexity of relational query languages. In: Proceedings of the 14th ACM Symposium on Theory of Computing, pp. 137–146 (1982)

    Google Scholar 

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Grohe, M. (2009). Fixed-Point Definability and Polynomial Time. In: Grädel, E., Kahle, R. (eds) Computer Science Logic. CSL 2009. Lecture Notes in Computer Science, vol 5771. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04027-6_4

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  • DOI: https://doi.org/10.1007/978-3-642-04027-6_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04026-9

  • Online ISBN: 978-3-642-04027-6

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