an:05315764
Zbl 1186.20041
Diekert, Volker; Lohrey, Markus
Word equations over graph products
EN
Int. J. Algebra Comput. 18, No. 3, 493-533 (2008).
00220342
2008
j
20M05 03B25 20F10 20E06 03D35 68Q70 68Q42 20F70 68Q25
equations in groups; equations in monoids; logical theories; graph products; decidability; algorithms; solvability of equations; existential theories; positive theories
The existence of algorithms recognizing the solvability of equations in a free semigroup was established by G. S. Makanin more than four decades ago and has prompted a wealth of research, well referenced in the paper under review. The authors continue this stream of research by establishing transfer results to graph products (a construction that generalizes both free and direct products) of monoids.
From the summary: ``For monoids that satisfy a weak cancellation condition it is shown that the decidability of the existential theory of word equations is preserved under graph products. Furthermore, it is shown that the positive theory of a graph product of groups can be reduced to the positive theories of those factors which commute with all other factors 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.''
Herman J. Servatius (Worcester)