Give a regular expression for the set of all binary strings where the second last

symbol is a $1.$ Explain your answer.

Construct a regular grammar for the set described in the question above.

Construct a regular grammar for the set of all binary strings that are of length two

or are of length three.

Study the definition of a right linear grammar and a left linear grammar. $($Both are

regular grammars.$)$ Then give a right linear grammar and separately a left linear

grammar for the set of all binary strings that have even length.

Show that the set $L=\{\begin{array}{c}{0}^0{1}^j\end{array}$ such that $\{$:$i>j\}$ is NOT regular. Hint: You will have to

"pump down" instead of pumping up$.$