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$1-$ Give the CFG rules for the following:

a$)$ Starts with $101$

b$)$ Has odd $1\text{'}$s

c$){00111}^n{0}^{2n}$

d$)1^n{01100}^n$

$2-$ Which of the following is a Regular Language? Prove or disprove

a$)$ LOLO where $L$ is the complement of regular language and $LO$ is a CFG

b$)$ LULO where $L$ is regular and $LO$ is a CFG

$3-$ Give a decision algorithm that takes a DFA M as input and decides whether:

a$)M$ accepts all strings with even $0\text{'}$s and ends with $101$

b$)M$ accept strings with length bigger than $6$