  The pressing need for efficient compression schemes for XML documents has
recently been focused on stack computation, and in particular calls for a
formulation of information-lossless stack or pushdown compressors that allows a
formal analysis of their performance and a more ambitious use of the stack in
XML compression, where so far it is mainly connected to parsing mechanisms. In
this paper we introduce the model of pushdown compressor, based on pushdown
transducers that compute a single injective function while keeping the widest
generality regarding stack computation.
  We also consider online compression algorithms that use at most
polylogarithmic space (plogon). These algorithms correspond to compressors in
the data stream model.
  We compare the performance of these two families of compressors with each
other and with the general purpose Lempel-Ziv algorithm. This comparison is
made without any a priori assumption on the data's source and considering the
asymptotic compression ratio for infinite sequences. We prove that in all cases
they are incomparable.
