Deadlock Detection for a Class of Communicating Finite State Machines

Let
M
and
N
be two communicating finite state machines which exchange one type of message. We develope a polynomial algorithm to detect whether or not
M
and
N
can reach a deadlock. The time complexity of the algorithm is
O(m^{3}n^{3}
and its space is
O(mn)
where
m
and
n
are the numbers of states in
M
and
N
, respectively. The algorithm can also be used to verify that two communicating machines which exchange many types of messages are deadlock-free.