You can write a function that recursively iterates through your nested listed and tries to convert each element to an iterator.
def recurse_iter(it):
if isinstance(it, basestring):
yield it
else:
try:
for element in iter(it):
for subelement in recurse_iter(element):
yield subelement
except TypeError:
yield it
This hideous function will produce a list of the strings and non-iterable members in an object.
a = [[1, [0], [0], [1, [0]]], [1, [0], [0], [1, [0]]], [1, [0], [0]]]
list(recurse_iter(a))
# [1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0]
Converting this to a string is straight forward enough.
''.join(map(str, recurse_iter(a)))