Labeling recursive auto-associative memory (LRAAM) is an extension of
the RAAM model by Pollack to obtain distributed reduced representation
s of labeled directed graphs. In this paper some mathematical properti
es of LRAAM are discussed, Specifically, sufficient conditions on the
asymptotical stability of the decoding process along a cycle of the en
coded structure are given, LRAAM can be transformed into an analog Hop
field network with hidden units and an asymmetric connections matrix b
y connecting the output units with the input units. In this architectu
re encoded data can be accessed by content and different access proced
ures can be defined depending on the access key, Each access procedure
corresponds to a particular constrained version of the recurrent netw
ork, We give sufficient conditions under which the property of asympto
tical stability of a fixed point in one particular constrained version
of the recurrent network can be extended to related fixed points in d
ifferent constrained versions of the network. An example of encoding o
f a labeled directed graph on which the theoretical results are applie
d is given and discussed.