$L = \{x\#w\mid w^R\text{ is a substring of }x\text{ for }x, w \in \{0,1\}^*\}$, where $w^R$ is denoted the reverse of string $w$
I am not sure
#means any valid string or just the number symbol itself ?What's the exact meaning of $w \in \{0,1\}^*$ ? it means $w$ can be any combination of $\{0,1\}$ including empty string?
Can empty string be the substring of any string by definition?
By the way, this $L$ can be transformed to a context free grammar.
Thank you all sincerely.
Actually it depends on the convention your textbook/course is following. In general, the following holds.
The implicit notion is that your alphabet is $\Sigma = \{0, 1, \# \}$. $\#$ is the symbol itself
For any alphabet $\Theta$, $\Theta^*$ denotes the set of all finite strings that can be constructed using alphabets in $\Theta$. Empty string $\epsilon$ belongs here.
Thus, $\{0, 1\}^* = \{ \epsilon, 0, 1, 00, 01, 10, 11, 000, 001, 010, 100, ... \}$
Yes