# The local-global property for G-invariant terms

@article{Kazda2022TheLP, title={The local-global property for G-invariant terms}, author={Alexandr Kazda and Michael Kompatscher}, journal={ArXiv}, year={2022}, volume={abs/2109.02065} }

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…

## Figures from this paper

## References

SHOWING 1-10 OF 26 REFERENCES

### DECIDING SOME MALTSEV CONDITIONS IN FINITE IDEMPOTENT ALGEBRAS

- MathematicsThe Journal of Symbolic Logic
- 2020

It is shown that for such “path defined” Maltsev conditions, the decision problem is polynomial-time solvable.

### Deciding the existence of quasi weak near unanimity terms in finite algebras

- MathematicsJ. Multiple Valued Log. Soft Comput.
- 2021

It is shown that for a fixed positive integer k one can efficiently decide if a finite algebra A admits a k-ary weak near unanimity operation by looking at the local behavior of the terms of A by looking for local quasi Siggers operations.

### Smooth digraphs modulo primitive positive constructability and cyclic loop conditions

- MathematicsInt. J. Algebra Comput.
- 2021

Finite smooth digraphs, that is, finite directed graphs without sources and sinks, can be partially ordered via pp-constructability. We give a complete description of this poset and, in particular,…

### The Subpower Membership Problem for Mal'cEV Algebras

- MathematicsInt. J. Algebra Comput.
- 2012

It is shown that the subpower membership problem for any finite Mal'cev algebra is in NP and a polynomial time algorithm is given for any infinite Mal'CEv algebra with finite signature and prime power size that has a nilpotent reduct.

### Idempotent n‐permutable varieties

- Mathematics
- 2014

One of the important classes of varieties identified in tame congruence theory is the class of varieties which are n‐permutable for some n . In this paper, we prove two results: (1) for every n>1,…

### The wonderland of reflections

- MathematicsArXiv
- 2015

A new elegant dichotomy conjecture for the CSPs of reducts of finitely bounded homogeneous structures is formulated and a close connection between h1 clone homomorphisms and the notion of compatibility with projections used in the study of the lattice of interpretability types of varieties is revealed.

### Pseudo‐loop conditions

- MathematicsThe bulletin of the London Mathematical Society
- 2019

Proving that for each fixed width m there is a weakest loop condition (that is, one entailed by all others), and obtaining a new and short proof of the recent celebrated result stating that there exists a concrete loop condition of width 3 which is entailed in any non‐trivial idempotent, possibly infinite, algebra.

### Asking the Metaquestions in Constraint Tractability

- Computer ScienceTOCT
- 2017

This article systematically studies—for various classes of polymorphisms—the computational complexity of deciding whether or not a given structure ℍ admits a polymorphism from the class, and proves the NP-completeness of deciding a condition conjectured to characterize the tractable problems CSP(ℍ).

### Computational Complexity of Various Mal'cEV conditions

- MathematicsInt. J. Algebra Comput.
- 2013

This paper defines a class of Mal'Cev conditions whose satisfaction can be determined in polynomial time (special cube term satisfying the DCP) when the algebra in question is idempotent and provides an algorithm through which this determination may be made.

### Complexity of Infinite-Domain Constraint Satisfaction

- Computer Science
- 2021

This monograph presents a self-contained introduction to the universal-algebraic approach to complexity classification, treating both finite and infinite-domain CSPs.