is already occupied by another $B$ particle, the two $B$ particles transmute to two $A$ particles which will be placed at two nearest neighbor sites. If any of transmuted $A$ particles is placed at the site already occupied by another $A$ particle, both particles are annihilated immediately. In summary, $2A\rightarrow\emptyset$, $A\rightarrow A+B$, and $2B\rightarrow 2A$ processes are allowed with $A$ particle diffusion.

Since $B$ particles are not allowed to hop, the system is inactive without an $A$ particle but only with $B$ particles. The number of the absorbing states grows exponentially with system size and the auxiliary field ($B$ particle) density is finite at the absorbing transition. Besides, the number of $A$ particles is conserved modulo 2, which is the characteristic of the DI (or parity-conserving) class.

As in Sec. \[Sec:dpima\], we study the crossover by introducing spontaneous annihilation of $B$ particles (inhibitory route) with rate $w$. As expected, we find the DI critical scaling for both $w=0$ and $w\neq 0$ cases. We locate the critical line by exploiting the known DI critical exponents [@DIPark], which is summarized in Table \[Table:DI\_pc\] for some $w$’s. Since the critical exponent $\nu_\|$ of the DI class ($\simeq 3.25$) is much larger than that 