📘 formal languages

1. **State the problem:** We have the grammar $S \to aSbS \mid bSaS \mid \epsilon$ and need to perform the leftmost and rightmost derivations for the string $abaab$.

1. **State the problem:** We need to write a context-free grammar (CFG) for the language $L = \{a \mid a \text{ contains equal number of } x\text{'s and } y\text{'s and the number

1. **Problem Statement:** Construct a regular expression (RE) for the language over the alphabet $\Sigma = \{0,1\}$ that accepts all strings starting with $1$ and ending with $00$.

1. **Problem Statement:** Construct a regular expression (RE) for the language over the alphabet $\Sigma = \{a,b,c\}$ that accepts all strings containing at least one $a$ followed