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تسجيل مستخدم جديدThe local-global property for G-invariant terms
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نشر من قبل
Michael Kompatscher
تاريخ النشر
2021
مجال البحث
الهندسة المعلوماتية
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English
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For some Maltsev conditions $Sigma$ it is enough to check if a finite algebra $mathbf A$ satisfies $Sigma$ locally on subsets of bounded size, in order to decide, whether $mathbf A$ satisfies $Sigma$ (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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