文章基本信息

标题：Canonization for Bounded and Dihedral Color Classes in Choiceless Polynomial Time
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作者：Moritz Lichter ; Pascal Schweitzer
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2021
卷号：183
页码：31:1-31:18
DOI：10.4230/LIPIcs.CSL.2021.31
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：In the quest for a logic capturing Ptime the next natural classes of structures to consider are those with bounded color class size. We present a canonization procedure for graphs with dihedral color classes of bounded size in the logic of Choiceless Polynomial Time (CPT), which then captures Ptime on this class of structures. This is the first result of this form for non-abelian color classes. The first step proposes a normal form which comprises a "rigid assemblage". This roughly means that the local automorphism groups form 2-injective 3-factor subdirect products. Structures with color classes of bounded size can be reduced canonization preservingly to normal form in CPT. In the second step, we show that for graphs in normal form with dihedral color classes of bounded size, the canonization problem can be solved in CPT. We also show the same statement for general ternary structures in normal form if the dihedral groups are defined over odd domains.
关键词：Choiceless polynomial time; canonization; relational structures; bounded color class size; dihedral groups