I've been learning on Formal Languages and Automata of Peter Linz(6th edition).
In the chapter 3 of this book, it explains the primitive regular expression.
But I don't know what is the difference between $\phi$ and $\lambda$.
Of course, I know $\lambda$ means the empty string, so that $\lambda s=s\lambda$.
And the textbook explains the meaning of $\phi$ is the empty set.
And more, the textbook explains that $\phi$ can be accepted by a deterministic finite automata $\left< Q, \Sigma, \delta, q_0 , F \right>$ in which $Q=\{ q_0, q_1 \}$, $\forall a \in \Sigma:\delta(q_0,a)\text{ is not defined}$, and $F=\{q_1\}$.
So, I guess the meaning of the $\phi$ is the rejected string.
But How can the expression $(\phi *)*$ mean $\lambda$?
And what's the meaning of the expression $a\phi$?