Fixed-point logics on planar graphs

被引：44
|
作者：
Grohe, M [1 ]
机构：
[1] Albert Ludwigs Universitat Freiburg, Inst Math Log, D-79104 Freiburg, Germany
来源：
THIRTEENTH ANNUAL IEEE SYMPOSIUM ON LOGIC IN COMPUTER SCIENCE, PROCEEDINGS | 1998年
关键词：
D O I：
10.1109/LICS.1998.705639
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
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 IFP. This answers a question of Dawar and Gradel [16].
引用
收藏
页码：6 / 15
页数：10
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