Polynomial-time tests for difference terms in idempotent varieties

DeMeo, William; Freese, Ralph; Valeriote, Matthew

doi:10.1142/s021819671950036x

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2021

2023

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Cited by 4 publications

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“…condition of height 1 [Kaz21]. In [FV09] and [DFV19] it was shown that also some nonstrong Maltsev conditions can be decided in polynomial time, by studying local conditions (i.e. properties of subalgebras with bounded generating sets).…”

Section: Introductionmentioning

confidence: 99%

The local-global property for G-invariant terms

Kazda¹,

Kompatscher²

2021

Preprint

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For some Maltsev conditions Σ it is enough to check if a finite algebra A satisfies Σ locally on subsets of bounded size, in order to decide, whether 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 ≤ 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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Section: Introductionmentioning

confidence: 99%