G-不变项的局部-整体性质
The local-global property for G-invariant terms
摘要：
对于某些Maltsev条件$Σ$，检查有限代数$\mathbf A$是否在有界大小的子集上局部满足$Σ$就足够了，以便决定$\mathbf A$是否满足$Σ$（全局）。这种局部-全局性质是决定Maltsev条件的易处理性结果的主要已知来源。本文研究了$G$ -项存在的局部-整体性质，即$n$ -元项在按照置换群$G \leq$ Sym（$n$）置换其变量时不变.我们的结果特别意味着，所有的循环回路条件（在Bodirsky，Starke和Vucaj的意义下）具有局部-全局性质（因此可以在多项式时间内决定），而对称项的arity $n>2$没有它。
英文摘要：
For some Maltsev conditions $Σ$ it is enough to check if a finite algebra $\mathbf A$ satisfies $Σ$ locally on subsets of bounded size, in order to decide, whether $\mathbf A$ satisfies $Σ$ (globally). This local-global property is the main known source of tractability results for deciding Maltsev conditions. In this paper we investigate the local-global property for the existence of a $G$-term, i.e. an $n$-ary term that is invariant under permuting its variables according to a permutation group $G \leq$ Sym($n$). Our results imply in particular that all cyclic loop conditions (in the sense of Bodirsky, Starke, and Vucaj) have the local-global property (and thus can be decided in polynomial time), while symmetric terms of arity $n>2$ fail to have it.
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