Problem $1$

Write a PDA that accepts the language of strings of $\{a,b,c\}$ where the number of instances of $ab$ is

equal to the number of instances of bc$.$

Problem $2$

Write a CFG that generates the language of strings of $\{a,b,c\}$ where there are more a$\text{'}$s before the

first $c$ than b$\text{'}$s after it$.$

Problem $3$

Let in $L,x$ and $z$ non$-$empty