Consider the following languages:
$${L_1} = \left\{ {w\,w\left| {w \in {{\left\{ {a,\,b} \right\}}^ * }} \right.} \right\}$$
$${L_2} = \left\{ {w\,{w^R}\left| {w \in {{\left\{ {a,\,b} \right\}}^ * },} \right.{w^R}\,\,} \right.$$ is the reverse of $$\left. w \right\}$$
$${L_3} = \left\{ {{0^{2i}}\left| {i\,\,} \right.} \right.$$ is an integer$$\left. \, \right\}$$
$${L_4} = \left\{ {{0^{{i^2}}}\left| {i\,\,} \right.} \right.$$ is an integer$$\left. \, \right\}$$

Which of the languages are regular?

What can be said about a regular language $$L$$ over $$\left\{ a \right\}$$ whose minimal finite state automation has two states?

Let $$L$$ be the set of all binary strings whose last two symbols are the same. The number of states in the minimum state deterministic finite-state automaton accepting $$L$$ is

Which one of the following regular expressions over $$\left\{ {0,\,\,1} \right\}$$ denotes the set of all strings not containing $$100$$ as substring?