AN AUTOMATA THEORETIC APPROACH TO THE GENERALIZED WORD PROBLEM IN GRAPHS OF GROUPS

Abstract. We give a simpler proof using automata theory of a recent result of Kapovich, Weidmann and Myasnikov according to which so-called benign graphs of groups preserve decidability of the generalized word problem. These include graphs of groups in which edge groups are polycyclic-by-finite and vertex groups are either locally quasiconvex hy-perbolic or polycyclic-by-finite and so in particular chordal graph groups (right-angled Artin groups). 1