  We study a version of compact directed percolation (CDP) in one dimension in
which occupation of a site for the first time requires that a "mine" or
antiparticle be eliminated. This process is analogous to the variant of
directed percolation with a long-time memory, proposed by Grassberger, Chate
and Rousseau [Phys. Rev. E 55, 2488 (1997)] in order to understand spreading at
a critical point involving an infinite number of absorbing configurations. The
problem is equivalent to that of a pair of random walkers in the presence of
movable partial reflectors. The walkers, which are unbiased, start one lattice
spacing apart, and annihilate on their first contact. Each time one of the
walkers tries to visit a new site, it is reflected (with probability r) back to
its previous position, while the reflector is simultaneously pushed one step
away from the walker. Iteration of the discrete-time evolution equation for the
probability distribution yields the survival probability S(t). We find that
S(t) \sim t^{-delta}, with delta varying continuously between 1/2 and 1.160 as
the reflection probability varies between 0 and 1.
