@article{doi:10.1142/S0218196706003372,
    Abstract = {We show that the existential theory of free partially commutative monoids with involution is decidable. As a consequence the existential theory of graph groups is also decidable. If the underlying alphabet of generators is fixed, we obtain a PSPACE-completeness result, otherwise (in the uniform setting) our decision procedure is in EXPSPACE. Our proof is a reduction to the main result of [6].},
    Author = {DIEKERT, VOLKER and MUSCHOLL, ANCA},
    EPrint = {https://doi.org/10.1142/S0218196706003372},
    File = {Solvability of equations in graph groups is decidable - s0218196706003372.pdf},
    Journal = {International Journal of Algebra and Computation},
    Number = {06},
    Pages = {1047-1069},
    Title = {SOLVABILITY OF EQUATIONS IN GRAPH GROUPS IS DECIDABLE},
    URL = {https://doi.org/10.1142/S0218196706003372},
    Volume = {16},
    Year = {2006},
    bdsk-url-1 = {https://doi.org/10.1142/S0218196706003372},
    date-added = {2023-08-09 16:06:17 +0200},
    date-modified = {2023-08-09 16:06:17 +0200},
    file-2 = {SOLVABILITY OF EQUATIONS IN GRAPH GROUPS IS DECIDABLE - dm05ijac.pdf},
    doi = {10.1142/S0218196706003372}
}

@article{doi:10.1142/S0218196706003372, Abstract = {We show that the existential theory of free partially commutative monoids with involution is decidable. As a consequence the existential theory of graph groups is also decidable. If the underlying alphabet of generators is fixed, we obtain a PSPACE-completeness result, otherwise (in the uniform setting) our decision procedure is in EXPSPACE. Our proof is a reduction to the main result of [6].}, Author = {DIEKERT, VOLKER and MUSCHOLL, ANCA}, EPrint = {https://doi.org/10.1142/S0218196706003372}, File = {Solvability of equations in graph groups is decidable - s0218196706003372.pdf}, Journal = {International Journal of Algebra and Computation}, Number = {06}, Pages = {1047-1069}, Title = {SOLVABILITY OF EQUATIONS IN GRAPH GROUPS IS DECIDABLE}, URL = {https://doi.org/10.1142/S0218196706003372}, Volume = {16}, Year = {2006}, bdsk-url-1 = {https://doi.org/10.1142/S0218196706003372}, date-added = {2023-08-09 16:06:17 +0200}, date-modified = {2023-08-09 16:06:17 +0200}, file-2 = {SOLVABILITY OF EQUATIONS IN GRAPH GROUPS IS DECIDABLE - dm05ijac.pdf}, doi = {10.1142/S0218196706003372} }