  Using Pade approximations and Monte Carlo simulations, we study the phase
diagram of the Two-Neighbor Stochastic Cellular Automata, which have two
parameters $p_{1}$ and $p_{2}$ and include the mixed site-bond directed
percolation (DP) as a special case. The phase transition line $p_{1}=p_{1 {\rm
c}}(p_{2})$ has endpoints at $(p_{1}, p_{2})=(1/2,1)$ and at (0.8092, 0). The
former point (1/2,1) is a special point at which Compact DP transition occurs
and its critical exponents are known exactly. Results of time-dependent
simulation show that in the whole range of parameters, excluding this point
(1/2,1), the system belongs to the DP universality class. It is first shown
that the shape of the phase transition line near this special point has,
asymptotically, a parabolic shape, {\it i.e.}, $p_{1{\rm c}}(p_{2})-1/2 \sim
(1-p_{2})^{\theta}$ with $\theta = 1/2$ for $0 < 1-p_{2} \ll 1$. We use the
Monte Carlo data to assess the accuracy of rigorous bounds for the line
recently reported by Liggett and by Katori and Tsukahara. It is also shown that
outside the vicinity of the special point (1/2,1), the curve is well
approximated by an interpolation formula, similar to the one proposed by Yanuka
and Englman.

Condensed Matter