  This paper considers a class of probabilistic cellular automata undergoing a
phase transition with an absorbing state. Denoting by ${\mathcal{U}}(x)$ the
neighbourhood of site $x$, the transition probability is $T(\eta_x = 1 |
\eta_{{\mathcal{U}}(x)}) = 0$ if $\eta_{{\mathcal{U}}(x)}= \mathbf{0}$ or $p$
otherwise, $\forall x \in \mathbb{Z}$. For any $\mathcal{U}$ there exists a
non-trivial critical probability $p_c({\mathcal{U}})$ that separates a phase
with an absorbing state from a fluctuating phase. This paper studies how the
neighbourhood affects the value of $p_c({\mathcal{U}})$ and provides lower
bounds for $p_c({\mathcal{U}})$. Furthermore, by using dynamic renormalization
techniques, we prove that the expected convergence time of the processes on a
finite space with periodic boundaries grows exponentially (resp.
logarithmically) with the system size if $p > p_c$ (resp. $p<p_c$). This
provides a partial answer to an open problem in Toom et al. (1990, 1994).
