Abstract
In this article, we define a new variant of Cai-Fürer-Immerman construction. With this construction and some conditions of Dawar and Richerby, we are able to show that inflationary fixed point logic with counting (IFP+C) does not capture PTIME on the class of balanced graphs.
Supported by the National Natural Science Foundation of China under Grant No. 60721061 and 60833001.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Brandstädt, A., Le, V.B., Sprinrad, J.P.: Graph Classes: A Survey. SIAM, Philadelphia (1999)
Cai, J.-Y., Fürer, M., Immerman, N.: An optimal lower bound on the number of variables for graph identification. Combinatorica 12(4), 389–410 (1992)
Chandra, A., Harel, D.: Structure and complexity of relational queries. Journal of Computer and System Sciences 25, 99–128 (1982)
Dawar, A.: Personal Communication
Dawar, A., Richerby, D.: The Power of Counting Logics on Restricted Classes of Finite Structures. In Proc. 16th EACSL Annual Conference on Computer Science Logic. In: Duparc, J., Henzinger, T.A. (eds.) CSL 2007. LNCS, vol. 4646, pp. 84–98. Springer, Heidelberg (2007)
Ebbinghaus, H.D., Flum, J.: Finite Model Theory, 2nd edn. Springer, Heidelberg (1999)
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)
Golumbic, M.C.: Algorithmic Graph Theory and Perfect Graphs, 2nd edn. Elsevier, Amsterdam (2004)
Grohe, M.: Fixed-point logics on planar graphs. In: Proc. 13th IEEE Annual Symposium on Logic in Computer Science, pp. 6–15. IEEE Computer Society Press, Los Alamitos (1998)
Grohe, M.: Isomorphism testing for embeddable graphs through definability. In: Proc. 32nd ACM Symposium on Theory of Computing, pp. 63–72. ACM Press, New York (2000)
Grohe, M.: Definable Tree Decompositions. In: Proc. 22nd IEEE Annual Symposium on Logic in Computer Science, pp. 406–417. IEEE Computer Society, Los Alamitos (2008)
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 (1988)
Hella, L.: Logical hierarchy in PTIME. Information and Computations 129(1), 1–19 (1996)
Immerman, N., Lander, E.S.: Describing graphs: A first-order approach to graph canonization. In: Selman, A. (ed.) Complexity Theory Retrospective, pp. 59–81. Springer, Heidelberg (1990)
Immerman, N.: Descriptive Complexity. Springer, Heidelberg (1999)
Otto, M.: Bounded Variable Logics and Counting – A Study in Finite Models. Lecture Notes in Logic, vol. 9. Springer, Heidelberg (1997)
Ramírez Alfonsín, J.L., Reed, B.A. (eds.): Perfect Graphs. John Wiley & Sons, Chichester (2001)
Seymour, P.D., Thomas, R.: Graph searching and a min-max theorem for tree-width. Journal of Combinatorial Theory Series B 58, 22–33 (1993)
Uehara, R., Toda, S., Nagoya, T.: Graph isomorphism completeness for chordal bipartite graphs and strongly chordal graphs. Discrete Applied Mathematics 145, 479–482 (2005)
Zhou, X., Wu, Z.: A Note on Using the Cops and Robber Game in the Bijection Game (Submitted)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Zhou, X. (2009). CFI Construction and Balanced Graphs. In: Deng, X., Hopcroft, J.E., Xue, J. (eds) Frontiers in Algorithmics. FAW 2009. Lecture Notes in Computer Science, vol 5598. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02270-8_12
Download citation
DOI: https://doi.org/10.1007/978-3-642-02270-8_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02269-2
Online ISBN: 978-3-642-02270-8
eBook Packages: Computer ScienceComputer Science (R0)