model itself in regard to the auxiliary field density.

To check the universality of the crossover exponent, we study the modified PCP with the replacement of $2A \rightarrow 3A$ with $3A
\rightarrow 4A$ in Eq.  which is the model of Eq.  with no diffusion ($D=0$). This model also has infinitely many absorbing states and belongs to the DP${}_\textrm{IM}$ class. By introducing single-particle reactions ($w\neq 0$), the same crossover behavior is found as the above (data not shown).

![\[Fig:TCPcollapse\] (Color online) Scaling plot of $\rho_t(t) t^{\delta}$ vs $w^{\mu_\|} t$ with the same exponents in Fig. \[Fig:mucollapse\] for the crossover TCP model of Eq.  in semi-log scales. As in Fig. \[Fig:mucollapse\], all curves are collapsed into a single curve.](ParkFig7.eps){width="45.00000%"}

We also study more general crossover behavior from one DP${}_\textrm{IM}$ to another DP${}_\textrm{IM}$ with the considerably reduced number of absorbing states. To be specific, we consider the triplet contact process (TCP) and its crossover model by introducing the $2A \rightarrow
A$ process without spontaneous death. The TCP with pair dynamics is defined as $$\label{Eq:TCPcross}
\begin{aligned}
&AAA \stackrel{p}{\longrightarrow} \emptyset \emptyset\emptyset,\quad
\left .\begin{matrix} AAA\emptyset\\ \emptyset AAA \end{matrix} \right \}
\begin{CD}
@>(1-p)/2>> AAAA,
\end{CD}\\
&\begin{CD}
 AA\emptyset
@>w/2>> A\emptyset \emptyset,\quad
\emptyset AA @>w/2>> \emptyset \emptyset A.
\end{CD}
