The Join Levels of the Trotter-Weil Hierarchy Are Decidable

@inproceedings{Kufleitner2012TheJL,
  title={The Join Levels of the Trotter-Weil Hierarchy Are Decidable},
  author={Manfred Kufleitner and Alexander Lauser},
  booktitle={MFCS},
  year={2012}
}
The variety DA of finite monoids has a huge number of different characterizations, ranging from two-variable first-order logic FO2 to unambiguous polynomials. In order to study the structure of the subvarieties of DA, Trotter and Weil considered the intersection of varieties of finite monoids with bands, i.e., with idempotent monoids. The varieties of idempotent monoids are very well understood and fully classified. Trotter and Weil showed that for every band variety V there exists a unique… 
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References

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