  In this work, we study the natural monotone analogues of various equivalent
definitions of VPSPACE: a well studied class (Poizat 2008, Koiran and Perifel
2009, Malod 2011, Mahajan and Rao 2013) that is believed to be larger than VNP.
We observe that these monotone analogues are not equivalent unlike their
non-monotone counterparts, and propose monotone VPSPACE (mVPSPACE) to be
defined as the monotone analogue of Poizat's definition. With this definition,
mVPSPACE turns out to be exponentially stronger than mVNP and also satisfies
several desirable closure properties that the other analogues may not.
  Our initial goal was to understand the monotone complexity of transparent
polynomials, a concept that was recently introduced by Hrube\v{s} and
Yehudayoff (2021). In that context, we show that transparent polynomials of
large sparsity are hard for the monotone analogues of all the known definitions
of VPSPACE, except for the one due to Poizat.
