A conjecture on the concatenation product

@article{Pin2001ACO,
  title={A conjecture on the concatenation product},
  author={Jean-{\'E}ric Pin and Pascal Weil},
  journal={RAIRO Theor. Informatics Appl.},
  year={2001},
  volume={35},
  pages={597-618}
}
  • J. Pin, P. Weil
  • Published 1 November 2001
  • Mathematics
  • RAIRO Theor. Informatics Appl.
In a previous paper, the authors studied the polynomial closure of a variety of languages and gave an algebraic counterpart, in terms of Mal'cev products, of this operation. They also formulated a conjecture about the algebraic counterpart of the boolean closure of the polynomial closure --- this operation corresponds to passing to the upper level in any concatenation hierarchy ---. Although this conjecture is probably true in some particular cases, we give a counterexample in the general case… 

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