  We develop an efficient algorithm to determine the memory-depth of finite
state machines and apply the algorithm to a collection of iterated prisoner's
dilemma strategies. The calculation agrees with the memory-depth of other
representations of common strategies such as Tit-For-Tat, Tit-For-2-Tats, etc.
which are typically represented by lookup tables. Our algorithm allows the
complexity of finite state machine based strategies to be characterized on the
same footing as memory-n strategies.
