  This paper studies left invertibility of discrete-time linear
output-quantized systems. Quantized outputs are generated according to a given
partition of the state-space, while inputs are sequences on a finite alphabet.
Left invertibility, i.e. injectivity of I/O map, is reduced to left
D-invertibility, under suitable conditions. While left invertibility takes into
account membership to sets of a given partition, left D-invertibility considers
only membership to a single set, and is much easier to detect. The condition
under which left invertibility and left D-invertibility are equivalent is that
the elements of the dynamic matrix of the system form an algebraically
independent set. Our main result is a method to compute left D-invertibility
for all linear systems with no eigenvalue of modulus one. Therefore we are able
to check left invertibility of output-quantized linear systems for a full
measure set of matrices. Some examples are presented to show the application of
the proposed method.
