  In this paper, 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 the 0-approximation [Son & Baral
2001] to define the regression function. In binary domains, the use of
0-approximation means using 3-valued states. Although planning using this
approach is incomplete with respect to the full semantics, we adopt it to have
a lower complexity. 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. We then develop a conditional planner that utilizes our
regression function. We prove the soundness and completeness of our planning
algorithm and present experimental results with respect to several well known
planning problems in the literature.
