The study of braid groups and their applications is
a field which has attracted the interest of
mathematicians and computer scientists alike. We
begin with a review of the notion of a braid group.
We then discuss known solutions to decision problems
in braid groups. We then prove new results in braid
group algorithmics. We offer a quick solution to the
generalized word problem in braid groups, in the
special case of cyclic subgroups. We illustrate this
solution using a multitape Turing machine. We then
turn to a discussion of decision problems in cyclic
amalgamations of groups and...