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Abstract: We study the expressive power of inflationary fixed-point logic IFP and inflationary fixed-point logic with counting IFP+C on planar graphs. We prove the following results: (1) IFP captures polynomial time on 3-connected planar graphs, and IFP+C captures polynomial time on arbitrary planar graphs. (2) Planar graphs can be characterized up to isomorphism in a logic with finitely many variables and counting. This answers a question of Immerman [7]. (3) The class of planar graphs is definable in... (Update)
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...in polynomial time. It reduces the algorithmic question to a de nability question. This method has successfully been applied to planar graphs [14] and graphs of bounded tree width [15] In this paper, we prove that for every (orientable or non orientable) surface S there is a k...
...to study particular, well behaved classes of structures. An example is the class P of planar graphs. It follows easily from the results of [10] that on P there is a P canonization function for L k equivalence (for each k) and an exponential upper bound for the size of the...
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0.3: Easy Instances for Model Checking - Frick (2001) (Correct)
0.3: The Building Blocks of Complexity: A Unified Criterion and.. - Seese, Schlottmann (2003) (Correct)
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0.5: On Fixed-Point Logic With Counting - Flum, Grohe (1998) (Correct)
0.5: Expressive Equivalence of Least and Inflationary Fixed-Point Logic - Kreutzer (2002) (Correct)
0.5: Fixed Point Logics, Generalized Quantifiers, and Oracles - Imhof (1995) (Correct)
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11: An optimal lower bound on the number of variables for graph identification - Cai, Furer et al. - 1992
11: Finite model theory (context) - Ebbinghaus, Flum - 1995
10: Relational queries computable in polynomial time - Immerman - 1986
BibTeX entry: (Update)
M. Grohe. Fixed-point logics on planar graphs. In Proceedings of the 13th IEEE Symposium on Logic in Computer Science, pages 6--15, 1998. http://citeseer.ist.psu.edu/grohe98fixedpoint.html More
@inproceedings{ grohe98fixedpoint,
author = "M. Grohe",
title = "Fixed-point logics on planar graphs",
booktitle = "proceedings of the 13th {IEEE} Symposium on Logic in Computer Science",
publisher = "IEEE Press",
pages = "6--15",
year = "1998",
url = "citeseer.ist.psu.edu/grohe98fixedpoint.html" }
Citations (may not include all citations):379 The complexity of relational query languages (context) - Vardi - 1982
245 Relational queries computable in polynomial time - Immerman - 1986 ACM DBLP
124 How to draw a graph (context) - Tutte - 1963
104 Springer-Verlag (context) - Diestel - 1997
98 An optimal lower bound on the number of variables for graph .. - Cai, Furer et al. - 1992 ACM DBLP
85 Upper and lower bounds for first-order expressibility (context) - Immerman - 1982
66 Describing graphs: A firstorder approach to graph canonizati.. - Immerman, Lander - 1990
63 Toward logic tailored for computational complexity - Gurevich - 1984
39 Expressibility as a complexity measure: results and directio.. (context) - Immerman - 1987
36 Graph Theory (context) - Tutte - 1984 ACM
21 Embeddings and minors (context) - Thomassen - 1995 ACM
15 An analysis of fixed-point queries on binary trees (context) - Lindell - 1991 ACM DBLP
10 Isomorphism of planar graphs (context) - Hopcroft, Tarjan - 1972
4 Automated Documentation and Mathematical Linguistics (context) - Livchak, model et al. - 1983
3 Graph minors III (context) - Robertson, Seymour - 1984
1 Available at http://speedy (context) - open, finite et al.
The graph only includes citing articles where the year of publication is known.
Documents on the same site (http://sun2.mathematik.uni-freiburg.de/home/grohe/pub.html): More
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Equivalence in Finite-Variable Logics Is Complete for Polynomial.. - Grohe (1996) (Correct)
Large Finite Structures with Few L k -Types - Grohe (1997) (Correct)
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