Exercise $6\mathrm{.}1\mathrm{.}1$: Suppose the PDA $P=(\{q,p\},\{0,1\},\{Z_0,x\},,q,Z_0,\{p\})$ has the following transition function:

$(q,0,Z_0)=\{(q,x{Z}_0)\}.$

$(q,0,x)=\{(q,xx)\}.$

$(q,1,x)=\{(q,x)\}.$

$(q,lon,x)=\{(p,lon)\}.$

$(p,lon,x)=\{(p,lon)\}.$

$(p,1,x)=\{(p,xx)\}.$

$(p,1,Z_0)=\{(p,lon)\}.$

Starting from the initial ID $(q,w,Z_0),$ show all the reachable ID's when the input $w$ is:

a$)01.$

b$)0011.$

c$)010.$

a$)(7,01,z_0)+(7,1,z_0)$