A State-Based Regression Formulation for Domains with Sensing
  Actions<br> and Incomplete Information
  We present a state-based regression function for planning domains where an
agent does not have complete information and may have sensing actions. We
consider binary domains and employ a three-valued characterization of domains
with sensing actions to define the regression function. We prove the soundness
and completeness of our regression formulation with respect to the definition
of progression. More specifically, we show that (i) a plan obtained through
regression for a planning problem is indeed a progression solution of that
planning problem, and that (ii) for each plan found through progression, using
regression one obtains that plan or an equivalent one.
