Word Equations over Graph Products

@inproceedings{Diekert2003WordEO,
  title={Word Equations over Graph Products},
  author={Volker Diekert and Markus Lohrey},
  booktitle={Int. J. Algebra Comput.},
  year={2003}
}
For a restricted class of monoids, we prove that the decidability of the existential theory of word equations is preserved under graph products. Furthermore, we show that the positive theory of a graph product of groups can be reduced to the positive theories of some of the factor monoids and the existential theories of the remaining factors. Both results also include suitable constraints for the variables. Larger classes of constraints lead in many cases to undecidability results. 

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