using pen and paper please

Draw a PDA for each of the following: Here, $=\{0,1\}$ or $\{a,b\}.$

$L=\{0^n{1}^m|nm\}$

$L=\{0^n{1}^m{0}^k|n+k=m\}$

$\{a^i{b}^j|0ij\}$

$\{a^i{c}^j{b}^i|i,j0\}$

Draw full$-$fledged $($all state$-$transitions$)$ decider TMs for each of the following:

The machine multiplies a binary number by $2.$ That is$,$ give a binary number

$\text{'}n\text{'}$ written on the tape of the TM$,$ the machine, once done, should leave

$2xn$ on the tape.

The machine for the language $L=\{\begin{array}{c}{a}^i{b}^j{c}^k\end{array},$ such that $\{$:ixj$=k\}.$

The TM$\text{'}$s task is to make a copy of that string and halt. If the machine is

started in state $g_s$ in the configuation $q_{s}1101B,$ the machine should halt

with the following tape contents $1101$$$1101B.$ That is$,$ the string $1101$ is

copied over with a $\text{'}$ $ $\text{'}$ in between the copies. $($here B means blank$)$