Conjugacy in Miller's groups (Q6654578)

Let \(G\) be a finitely presented group, \textit{C. F. Miller III} [On group-theoretic decision problems and their classification. Princeton, N. J.: Princeton University Press and University of Tokyo Press (1971; Zbl 0277.20054)] associated to it a finitely generated free-by-free group \(M(G)\), known as the Miller Machine, whose conjugacy problem is closely related to the conjugacy and word problems of \(G\).\N\NIn the paper under review the author reduces the conjugacy problem in \(M(G)\) to a strong form of list conjugacy in \(G\), which he calls iso-computational list conjugacy. He proves that if \(G\) is finite, the conjugacy problem for \(M(G)\) is in \textsf{PSPACE}.