Give informal English descriptions of PDAs for the following languages.
- The set of strings over the alphabet $\{a,b\}$ with more $a's$ than $b's$
- The complement of the language $\{a^{n}b^{n}|n\geq 0\}$
- $\{w\#x|w^{R}$ $\text{is a substring of $x$ for }$ $w,x \in\{0,1\}^{*}\}$
- $\{x_{1}\#x_{2}\#...\#x_{k}|k\geq 1,$ $\text{each}$ $ x_{i}\in\{a,b\}^{*},$ $\text{and for some i and }$ $ j,x_{i}=x_{j}^{R}\}$