Weakly Iterated Block Products and Applications to Logic and Complexity

@article{Straubing2010WeaklyIB,
  title={Weakly Iterated Block Products and Applications to Logic and Complexity},
  author={Howard Straubing and Pascal Tesson and Denis Th{\'e}rien},
  journal={IJAC},
  year={2010},
  volume={20},
  pages={319-341}
}
Unlike the wreath product, the block product is not associative at the level of varieties. All decomposition theorems involving block products, such as the bilateral version of Krohn–Rhodes’ theorem, have always assumed a right-to-left bracketing of the operands. We consider here the left-to-right bracketing, which is generally weaker. More precisely, we are interested in characterizing for any pseudovarieties of monoids U, V the smallest pseudovariety W that contains U and such that W V = W… CONTINUE READING

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